Fenny - Pureheart

Fenny - Pureheart is not currently available as a Trial Operative in any story mission, so if you don't have her the only way to try her is to wait for her banner so she has a trial.

Pureheart does very high damage, can have amazing mobility, has great AoE and single-target capabilities and can swap between them at-will, but that comes at the cost of her gameplay potentially feeling very clunky, the constant clicking and button mashing she requires, as well as the poor survivability that can potentially come from Pureheart constantly leaping into melee range of enemies, although spending most of her time airborne and out of the way of enemy attacks can give her decent overall survivability.
Her shots and skills auto-seeking can make her easy to play, but means the game might not target the enemy you want.
Pureheart also doesn't any way of supporting her teammates at all, and she isn't the easiest operative to build a team around.

TL:DR:

Role: Main DPS
Deals Thermal Damage
Her standard LMB rotation deals almost entirely Skill Damage, but does a little bit of Ballistic Damage as well.
If using her RMB attack combo only, then she deals Skill Damage only.
Can stay airborne for long periods.

How to use Fenny - Pureheart

Against single-targets (or 1 strong target with some trash mobs):
1. Use her Standard Skill, which will cause her to to leap to the target, deal damage, and enter the Aerial Purity state.
2. Shoot enemies with her LMB attack until Pureheart shoots her "Passion Sparkshot", which gives 1 Passion Propulsion if it hits
(Passion Propulsion = The three bars around the edge of the gauge she has in the centre of the screen. They turn orange when charged.)
3. Repeat steps 1 and 2 until she has three Passion Propulsion, then use her Standard Skill and immediately use her ult
Repeat

You will normally have to do steps 1 and 2 three times, but if you miss a Passion Sparkshot you won't gain a Passion Propulsion, and hence will need to repeat steps 1 and 2 until you have the three Passion Propulsion required to use her ult.
Note that the 10 shots from her LMB attack do count as regular ballistic shots, and do not count as a skill use.
This rotation should take around 11 seconds.

If you are up against a group of multiple strong enemies:
1. Use her Standard Skill to enter Aerial Purity state and go airborne.
2. Press RMB until either everything dies or Pureheart is about to the floor.
Repeat
This rotation deals entirely skill dmg.
This rotation deals less single-target damage than her LMB combo, so only use this rotation against groups of multiple strong enemies where you need more AoE damage.

How to build Fenny - Pureheart

Weapon: Welkin Starflare is her ideal weapon, but if you don't have that then use Honeycomb.
Weapon Parts: Max ATK
Logistics Squad: Sprout
Basic Talent: +10.0% ATK
+106 Alignment Index
Special Talent: +8.5% Thermal Damage
Best Supports: Siris - Freefin
Vidya - Celestial Swan
Other supports

Specifics:

Standard Skill

Pureheart leaps to the target.
This does have quite a high range, and this allows Pureheart to close gaps incredibly well.
Since it only targets enemies, it can't be used as a generic movement ability in the same way that for example Turbo or Dawnwings abilities can.
This does also give a small amount of slow-mo after it is used.
Once at the target, she then throws a "Heartburst Ball" (a.k.a. "big bomb") at the group, the explosion of which blasts Pureheart into the air.
With her Neuronic, this also inflicts a 5s DoT.
Yes, you can use this to get on top of obstacles that melee enemies can't get on top of, meaning they can't hit you.
This isn't actually that useful in basically any gameplay, but it's worth noting.
After blasting herself into the air, Pureheart enters "Aerial Purity" state.
Entering Aerial Purity state automatically fully refills her Stamina and fully reloads her magazine.

Note that you can just spam her Standard Skill to repeatedly leap at the targeted enemy and bomb them.
Since this deals AoE damage, this is a perfectly viable way of clearing groups quickly, albeit not optimally.
It does have auto-aim though, so you can just spam the E key and everything will die eventually. Fun, but again - not optimal.

Whilst in Aerial Purity state, Pureheart can't be CC-ed, and can:

Do nothing and just fall back to the ground.
There is never a reason to do this in combat, but you could.
Right-click to throw a bomb to deal AoE damage
These bombs seek out nearby targets, meaning that provided you're aiming in the vicinity of an enemy you'll never miss.
(Although since they're AoE bombs that's actually not much of a benefit...)
These don't count as Standard Skill uses.
Left-click to shoot her gun at enemies
These LMB shots do count as shot hits, and can proc shot effects like aptitude buffs, but they don't count as Standard Skill uses.
These shots automatically gain Thermal Aptitude, causing them to deal more Thermal DMG than normal.
Note that Pureheart can have multiple Thermal Aptitude buffs at the same time, so her shots can make use of both her own and Little Sunshine's Thermal Aptitudes.
These shots seek out nearby targets, meaning that provided you're aiming in the vicinity of an enemy you'll never miss.
They can still be blocked by terrain though, and won't auto-aim if you aren't looking near a valid target.

Each shot that Fenny shoots will charge the gauge in the centre of the Purehearts screen.
Once the gauge is full, Purehearts next shot will be a "Passion Sparkshot", which uses the rest of all of her magazines (including special mags) to fire one strong shot
It takes 10 shot hits to generate enough to fire a Passion Sparkshot.
This final Passion Sparkshot deals around 21.5x more damage than her other shots, or around 2.15x the damage of all 10 of her other shots combined.
This final shot hitting its target also generates 1 Passion Propulsion (which is used for her ult).
If this shot fails to deal damage to an enemy, then you don't get any Passion Propulsion.
If it hits terrain, if there's no target because everything's already dead, if you just look in the wrong direction - the reason doesn't matter. No hit = no charge.
Note that whilst the visual animation of Passion Sparkshot is quite large, it has no AoE.

Note that counter-intuitively the Passion Sparkshot counts as a skill hit, and is not a ballistic effect.
This means it isn't buffed by things like aptitude, but is buffed by skill damage buffs like M2 Riptide.

After using her Passion Sparkshot, Pureheart's LMB attack will have a brief lockout period that prevents her from using it briefly.
Pureheart will thus fall to the ground after using her Passion Sparkshot, but you can use her standard skill, use her RMB attack, or use her dodge to stay in the air.
This is the games hint as to what her rotation is - use her LMB attacks to charge up, and then you can use the standard skill to leap again, thus staying airborne.
Her Neuronic also gives her -50% Final DMG Taken during her next leap, which is a very nice damage reduction, as well as another hint as to how to play her.

Using either the LMB or RMB attack will cause Pureheart to fall slightly after each shot.
Aerial Purity state ends when Pureheart touches the ground.
Not "Reaches equal height to where she started", but "when she touches the ground".
With enough distance to fall, Pureheart can stay airborne using her RMB attack for an extremely long time, even with no enemies nearby.
By using her standard skill occasionally to re-gain height, Pureheart never needs to touch the ground at all - she can stay in the air indefinitely provided she has an enemy nearby to occasionally use her standard skill against.

Using either LMB or RMB during her during Aerial Purity will propel Pureheart backwards slightly.
If you are holding down a movement key, she will instead move in that direction.

Whilst in the air, Pureheart can dodge to quickly move in the given direction (or by-default forwards if you aren't holding a direction key).
Regardless of which direction you dodge in, Purheart maintains her vertical height whilst dodging.
Pureheart doesn't regen Stamina whilst in the air, so you get two dodges whilst in the air, regardless of how long you are airborne for.

Note that melee enemies can't attack Pureheart whilst she is in the air.
Being airborne also allows her to simply fly over certain enemy attacks.

Support Skill

Pureheart's Support Skill causes Pureheart to swap in and use her Standard Skill, leaping to the targeted enemy, dealing AoE damage, and entering Aerial Purity state as usual.

This means that Pureheart really doesn't have any support capabilities at all.
She could theoretically be used as or alongside a sub-DPS, as she can quickly and easily swap in and get her damage rotation up and running, but if you have another main DPS you want to be your only DPS, then Pureheart offers them absolutely nothing as a support operative.

Ultimate Skill

Once Pureheart has 3 Passion Propulsion, she can fire a huge bomb in front of her, dealing AoE Thermal Damage and knocking up to 5 enemies into the air.
If Pureheart has more than 50 U-Energy (40 with the Neuronic) when using her ult, the bomb consumes all U-Energy to deal more damage based on how much extra U-Energy was used.
Pureheart's standard LMB rotation doesn't generate much U-Energy, so Pureheart dealing extra damage if her U-Energy is above 50 isn't something that will trigger that often.
Similarly, her Neuronic reducing the cost of her ult from 50 to 40 U-Energy only results in a tiny average damage boost.

With her other Neuronic, the bomb also deals 20% more damage if used during Aerial Purity, which is a very nice damage boost.

The damage of this skill is actually quite high, although since Pureheart can't get to above 50 U-Energy each ult it's dps is not as high as you might think.
Its U-Energy cost of 0 and 5s cooldown makes it theoretically very spammable, but in practice it's entirely limited by how quickly Pureheart can generate Passion Propulsion.

Also yes, Purehearts ult is a huge AoE blast, but you can only charge her ult by using her LMB single-target-only attack - her AoE RMB attack doesn't charge her AoE ult.

Pureheart can't generate Passion Propulsion unless she is on the field.
This means that if Pureheart is never put on the field then she can never generate the Passion Propulsion charges to use her ult at all, regardless of how much U-Energy you have.
This makes Pureheart a very poor support, as Purehearts ult is literally useless unless Pureheart herself is actually on the field generating charges.

Weapon

Welkin Starflare
Her 5* weapon, and her best weapon.
Grants Thermal DMG, Skill DMG, and extra Skill DMG taken.
All pretty standard for a new operative-specific 5*, but it works very well.
Honeycomb
Her 4* event weapon.
+ATK after using an Active Skill and +3% Thermal DMG for 10s (up to 5 stacks) after shooting.
This means Honeycomb tends to work better for LMB attacks than RMB, due to the RMB attack not giving the Thermal DMG buff.
It's not enough of a difference that you'd change which attack you use just to get the buff, but it is notable as buffing her LMB combo more than her RMB attack.

For weapon Parts just go with max ATK.

Logistics

Use Sprout squad - it was designed specifically for her and is her best choice.

For stats you want +10.0% ATK and +106 Alignment Index.
For the Special talent, you want +8.5% Thermal Damage

Alignment gives her more ATK.
(A max-roll of 106 Alignment Index gives Pureheart +5.3% ATK)

Her standard skill having a cooldown of 1 second (and being limited by animation speed anyway) means that Skill Haste is useless.
Similarly, her Support Skill just swaps her in, so there's absolutely no reason for it to have Skill Haste.
Since her LMB shots are shots and not skills, they are unaffected by Skill Haste.
Her standard skill having an S-Energy cost of 0 means that S-Energy regen is literally useless.
Being a largely skill-based dps means that crit rate and crit dmg amplifier are extremely bad to her as skills can't crit.
Her LMB shots can crit, but her base crit rate is 0% so she can only actually crit if shooting a weakspot (as weakspot hits always crit), and since she has a base crit damage of a paltry 30% Crit Dmg Amplifier mods don't buff her crits very much.
Pureheart doesn't heal or create shields, so those stats are also useless to her

Her ultimate skill having a U-Energy cost of 0 means that U-Energy regen is literally useless for spamming her ult.
U-Energy regen is useful though since her ult gains extra damage from being used at higher U-Energy levels.
The extra U-Energy that a U-Energy Regen stat would give is very small, and it's a very bad stat for Pureheart, but it does actually help her.
...if she's using LMB attacks.
If you're just spamming RMB attacks with Pureheart then U-Energy Recovery is literally useless as well, as you can't charge or use her ult with RMB attacks.

This means that U-Energy regen is Pureheart's only cope stat.
Other than ATK, Alignment Index, Thermal DMG, and U-Energy Recovery all other stats are either functionally worthless or literally worthless to Pureheart.

Manifestation

M1 gives Purehearts standard skill and support skill an extra 18% Skill DMG taken modifier for 5s.
Given how rare DMG Taken modifiers are, this is actually extremely strong, especially for an M1, if you're using her LMB attack.
M1 is not as useful for her RMB though as you want to use her standard skill less for her RMB combo, as the RMB attacks deal more damage than the standard skill.
This means that if using her RMB attack you want to use her standard skill every 5s to maintain the M1 buff, but otherwise keep using the stronger RMB attack.
M2 gives each LMB attack a -5% DEF debuff for 3s, up to 4 stacks.
If Pureheart is just spamming her LMB attack this is quite a nice buff.
Given how rare -DEF is, this is actually pretty strong.
If spamming her RMB attack though, M2 is literally useless.
M3 gives Pureheart +10% Final DMG dealt to all targets inflicted with the DoT from her standard skill activations Neuronic Effect.
This only applies if Pureheart has a Thermal Weapon equipped, but if you've gotten her to M3 she should always have a Thermal weapon equipped.
Remember that the DoT lasts 5 seconds.
Whilst +10% Final DMG is nice, this does mean that you will want to use her Standard Skill every 5s or more often in order to get this M3 damage bonus.
For her standard skill/LMB/Ult combo this is fine, and she should be doing that anyway.
For her RMB combo there's no need to use her standard skill at all except for her M1 since her RMB attack deals more damage than her standard skill.
You either use a weaker attack to apply the M1 and M3 buffs, or you ignore her M1 and M3 buffs entirely and just continue using her stronger RMB. Both feel bad.
M4 gives her standard skill +1 level with the usual +10% damage buffs.
This is basically the same as the M4 buff all other operatives have gotten for a long time now. It's fine.
M5 just gives her +20% ATK whilst in Aerial Purity state.
Since she should always be in Aerial Purity state whilst in combat, this is basically a permanent 20% ATK buff., which is very nice.

If you want efficiency (good damage with minimal investment), then M1 and M3 are good stopping points.
M3 if you're using the LMB combo, but if you often find yourself only using the RMB attacks then M1 is also a very good stopping point.

Good Supports for Fenny - Pureheart

Siris - Freefin
Freefin is a pure skill-dmg buffer who doesn't buff ballistic damage, but she's still Pureheart's best support.
Freefin is also on-element with Pureheart, and can thus work perfectly with Celestial Swan.
Vidya - Celestial Swan (and other resistance shredders)
Celestial Swan and other resistance shredders (Acacia - Kaguya, etc.) that reduce the enemies resistance help enemies take more damage.
If using Celestial Swan, make sure the other support isn't off element to Pureheart (i.e. they deal Thermal damage).
Eatchel - The Cub
A Blitzing Fangs Eatchel provides a nice ATK boost, as well as the passive healing.
Given that Pureheart needs to be near enemies to deal damage, she can be quite squishy, which Eatchel's healing massively helps with.
Tess - The Magician
Purehearts ult benefits from having lots of U-Energy, and having Tess give a lot of it allows Pureheart more damage for her ult.
Whilst using Tess to generate U-Energy quickly works for many operatives like Hush and Tempest, Pureheart still has a long windup before she can use her ult.
This makes (Pureheart + Tess) a thermal-damage and slower version of (Tempest + Tess), although Pureheart + Tess is great for short content where one ult is enough.
Pureheart + Tess can work, but does require very high investment into both operatives, and ideally a good 3rd operative too.
Tess doesn't add much to Purehearts sustained dps, making her a poor choice for Supreme Battleground or other longer content.
Marian - Riptide
Pureheart benefits from Marians Skill DMG and ResPen buffs
Being off-element means that Riptide is not a good choice if used with Celestial Swan, but otherwise Marian works well.
Pureheart's Support Skill does allow her to get back into her damage rotation pretty much immediately after Marian is finished magdumping.
This means Pureheart + Riptide does actually work very well.
Since Purheart's LMB and RMB attacks don't count as skill uses though, they won't generate any Tidesong for Riptide.
It's not very effective, but as cursed as it sounds you can just spam Pureheart's standard skill repeatedly, which will charge Riptide's Tidesong quite quickly.
It's not an ideal rotation or operative pairing, but in a pinch it can work.
Note that Riptide can't fly, and will fall to the group if you use Riptide's support skill whilst Pureheart is airborne.
Riptide having to recover after hitting the floor loses you like a second, which does add up over many rotations.
As such, you should use Riptide's support skill after Pureheart uses her ult and is already on the ground.
You can do two rotations of Pureheart's LMB combo, then after Pureheart's ult you can swap Riptide in to magdump, then swap Purehart in via her support skill.
Mauxir - Shadow Ka
Shadow Ka's utility is mostly useless to Pureheart due to Purehearts AoE and her shots auto-seeking, however the extra damage is nice.
Enya - Exuvia
Her Skill Dmg buffs are very much appreciated by Pureheart, and Pureheart's LMB combo does shoot a lot to charge Exuvia's Zephyr Machine.
Purehearts skills don't do enough skill hits to make good use of Exuvia's buff though, making Exuvia only a decent support overall.

Cope Supports - I.e. you don't have the above, but you want her to have something:

Yao - Nightglow
Nightglow is decent overall, but only her LMB attacks actually benefit from Yao's ballistic buffs, meaning most of Purehearts damage isn't affected by them
Skills can't crit, and Pureheart has a 0% crit rate, so unless she's shooting at a weakspot Yao's crit weakness mods are utterly useless to Pureheart.
Yao's ATK bonus is still good, but that alone isn't amazing on its own, and it makes Nightglow something of a cope support for Pureheart.
Tess - Phantasia and Fritia - Little Sunshine
Pureheart's LMB combo does shoot a decent number of shots.
Pureheart doesn't fire that many shots when compared to a lot of other operatives, but it's not the worst RoF.
For reference, Pureheart fires 30 shots over her 11s rotation, for an average of around 2.7 shots/second.
By-comparison, Wednesday using Work-in-Progress fires 11.1 shots/second (after factoring in reloading), which is a little over 4x more.
Chenxing - The Observer
With her M3 (and ideally M5) buffs, Chenxing provides some nice skill damage buffs that Pureheart appreciates.
She's not the strongest, but certainly decent.
Vidya - Agave
Basically a passive 20% ATK bonus. Decent, but not nearly as strong as the above.
A 15s buff on a 15s duration means it has basically 100% uptime though.

Overall

Fenny - Pureheart is... a mixed bag.

She's very certainly very strong if used properly, she can have good mobility, has strong AoE and single-target capabilities.
In practice though, having to use her single-target attack to charge up her AoE ult can feel clunky, as can the fact that her AoE attack doesn't charge up her AoE ult.

Her LMB attack dealing shot damage whilst her RMB attack is skill-only also makes her extremely clunky to use, as you may need to basically pick whether you want to use her LMB/RMB attack or not ahead of time so you can select supports appropriately.
You can use some supports regardless, but for some supports like Exuvia or The Magician you really do need to know what you are going to do ahead of time to know if she'll work.
Similarly, some of her Manifestations (and even her 4* weapon) buff her LMB or RMB, rather than buffing all of her capabilities.

This in-essence means that Pureheart can function as a hybrid dps, using her standard skill, LMB attack, and ult, with the LMB attacks being shots and the standard skill and ult being skills.
Alternatively, she can be run as a pure-skill dps, using just her standard skill and RMB attack.
She just can't really be run as both a hybrid or a pure skill dps at the same time though.

The easiest way to build Pureheart is to treat her as just a pure skill dps, ignoring the ballistic damage from her shots, but that does limit her potential supports a little.

Her support skill isn't really a support skill as much as it is just shaving a second or two off her standard rotation if using a sub-DPS, which is incredibly niche.
Whilst it's useful if using Marian - Riptide, it's not currently useful otherwise.
Hopefully Siris - Freefin can use that in some way.

If I had to give her a TL:DR, I'd say Pureheart is "strong but can feel clunky".