Tess - Phantasia

If you don't have Tess - Phantasia yet but want to try her out, she is available as a Trial Operative in Story Mission 15B-9 (Journey - Philossia - Concord Ode // "Endgame").

As a support operative Phantasia provides very strong per-shot frost damage, allowing her to add significant amounts of damage to high-RoF dps operatives.
Despite being best used as a support operative, Phantasia does also work quite well as a main dps, putting out decent damage [for a support operative].

Overview

Role: Support - Adds Frost damage to shots
Deals Frost Damage
Deals ballistic
Mobility is good

How to use Tess - Phantasia

As a support:

Use her ult immediately upon the fight starting
Spam her standard skill off-cooldown

As a DPS [Vs Single-Target]:

Use her standard skill to change her Apple to Red.
Hold her standard skill to spam her Red Apple buff every 15s
Otherwise shoot stuff.

As a DPS [Against Groups]:

Use her standard skill to change her Apple to Gold.
Hold her standard skill to lob her Gold Apple at a group of enemies. Repeat every 5s.
Shoot the enemies that were hit by the apple.

How to build Tess - Phantasia

Weapon: Valiant Heart / Confetti Chroma
Weapon Parts: Max ATK
Logistics Squad: Arcane
+10.0% ATK
+106 Alignment Index
+8.5% Frost Damage
Best teammates:
Katya - Rhapsody
Any other operative with a high Rate-of-Fire
(but ideally those dealing Frost damage)

Character Specifics:

Passive Effects

If she has a Frost-damage weapon, then Tess' Deiwos provides a 10% full-squad damage increase, plus 1% per 100 Alignment Index.
This bonus is doubled for allies dealing Frost damage.

Standard Skill

Tess always has a floating Apple by her side, which can provide her with a buff based on the Apples colour.
Using Tess' standard skill changes the colour/buff of the apple, cycling between Green -> Red -> Gold
Once Tess has the Apple colour you want, hold Tess' standard skill to then have her apply the Apple's buff:

Green
+1 S-Energy regen per sec
+50% Movement Speed for Tess and nearby allies.
The Green Apple doesn't use any S-Energy
Red
Hold her standard skill to have the Apple add Frost-damage to each of Tess' shots.
This buff lasts 15s, but can be immediately re-applied when it ends.

Note that the Red Apple buff adds 40% of Tess' ATK to each shot - it is not a +40% damage boost.
Given that Tess' designated Assault Rifles max out at 32.78% Weapon Compatibility, this means that the Red Apple buff will by-default more than double Tess' damage.
In practice it might be less depending on what specific buffs Tess has, but it's still a huge damage buff.
Alternatively, with her Red Apple buff, Tess does around 72.78% ATK damage. Factoring in her reload time both her designated AR's fire at exactly 10.0 shots per second.
This means that if just shooting enemies with her Red Apple buff, Tess' damage averages out to 727.8% ATK per second (before other buffs)
This, again, gives Tess very high dps for a support operative.
Gold
Hold her Standard Skill to have Tess hit her Apple at the enemy, dealing AoE Frost damage and knocking them into the air. This also marks them for 5s.
The Gold Apple does home in on a nearby enemy, so it'll still connect as long as you're aiming vaguely near an enemy.
This also means that Tess can hit targets even at quite long range.
When Tess shoots a marked enemy, she deals Frost damage to all marked enemies, with a cooldown of 2s.
This allows Tess to throw her Apple at a group of enemies, mark them all, then shoot one to deal damage to all of them.
Both the initial inpact and the group-damage deal around 16x the damage from a shot from Tess' Assault Rifle.

Alternatively, you can just have Tess continually lob her Gold Apple at a group of enemies to deal AoE damage and shoot once to proc the AoE damage.
This can clear groups very quickly, but will also drain Tess S-Energy extremely quickly as well, so only do this if you know you can kill the group in a few hits.

The damage bonus from Tess' Red Apple and the hit and mark damage from her Gold Apple are both high, and despite being a support operative, Tess does still deal decent damage in her own right.

Using Tess' Standard Skill to activate the Red and Gold Apple buffs costs 10 S-Energy.
For the Red Apple this is fine, as it has a 15s duration, and hence Tess will regenerate more S-Energy over its duration than she uses to cast it.
For the Gold Apple, Tess will run out of S-Energy over prolonged fights.
If Tess is up against such a strong group of enemies, you probably should have bought a proper main DPS rather than using Tess, as Tess is primarily a support, not a dps.

Support Skill

Tess gives the operative "Glimmerburst" for 12, which is a Frost aptitude that gives extra Frost damage per-shot.

Frost aptitude (extra Frost damage per shot)

Whilst it is active and Tess has dealt 100 instances of aptitude damage, Tess inflicts "Frostbite" for 2s, which deals Frost damage every 1s.
Frostbite can be proc'd once per support skill use.

Note that the 10s cooldown of this skill only starts when the 12s Glimmerburst duration ends.
This means that Tess doesn't run into any S-Energy issues.
Even if used during her ult (i.e. hopefully always) which reduces the cooldown to 5s due to the Neuronic buff, that's still 15 S-Energy every 17s, which is also fine.

Note also that the extra Frost damage is 30% of Tess' ATK, which means that the amount of damage Tess adds is about the same as what a regular SMG deals, and Tess can potentially provide a lot of extra damage to operatives with a high RoF.

TL:DR: Extra Frost damage for each shot, with high-RoF operatives gaining a few extra instances of damage.

Ultimate Skill

Tess creates a "Realm of Wonder" - a very large AoE that provides extra Frost aptitude damage and a ballistic damage buff to allies within it.
If Tess is your current operative then another operative will swap in - whilst her ult is active Tess can't be used as your deployed operative.
If Tess is your only operative, then Tess will stay in and create the Realm of Wonder as normal.

By-default Tess' ult lasts 12s, but with its first Neuronic it lasts forever.
Since it has a U-Energy cost of 0 and a 5s cooldown, this is not the most massive buff ever, but it is a very nice QoL chance.

By-default Tess' ult is a stationary AoE, but with its second Neuronic it will slowly move to follow you.

If Tess' support skill is also active, then Tess inflicting a target with the Frostbite effect from her support skill will increase the duration of her support skill by 3s.
This can potentially allow Tess unlimited duration on her support skill, but requires dealing 100 instances of aptitude damage in 3s, which requires a rate of fire of 34 shots per second or more. Currently the only operative who can produce such a high Rate-of-Fire is Katya - Rhapsody. For other operatives this can extend the duration of her Support Skill, but not indefinitely.

Weapon

Valiant Heart
Her 5* weapon, and her best weapon.
Gives Tess an ATK buff, gives a ballistic DMG buff when Tess is off-field.
Valiant Heart also inflicts Frostbite itself every 2s, and gives a full-squad ballistic and frost aptitude damage buff while Frostbite is active.
While Frostbite is active, the frost aptitude and ballistic damage also ignores some of the enemy DEF, which is Valiant Heart's main strength.
Confetti Chroma
Her 4* event weapon.
After dealing 200 instacnes of aptitude damage during Tess' support skill, inflicts Frostbite for 2s, which isn't that good since it can only be triggered once per skill use.
Confetti Chroma does give a nice ATK and ballistic damage buff during Tess' ultimate skill though, which is very nice.

For weapon Parts just go with max ATK, as the damage from Tess' Aptitude buffs scales off of Tess' ATK stat.

Logistics

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

For stats Phantasia wants 10.0% ATK and +106 Alignment Index.
For the Special talent, she wants 8.5% Frost Damage.

ATK both lets Tess herself deal more damage, but since the damage of her Aptitude buffs is based on her ATK, Tess wants as much ATK as possible.

Alignment Index gives Tess more full-squad damage, which doubles for Frost-damage operatives.
A max-roll of +106 Alignment Index gives the full-squad +1.06% damage, or +2.12% for Frost-damage operatives.
For three max-rolls, that is +3.18%, or + 6.36% for Frost-operatives.

For her special state, Tess wants +Frost Damage.

If used as a support, no other stat actually benefits her - Tess has no S-Energy issues, can't use U-Energy, and doesn't heal or create shields.

If used as a main-dps, then Crit Rate and Crit DMG Amplifier are both useful, but since most of Tess' damage will come from her Red Apple aptitude damage, whcih can't crit, and her base crit rate is 0% and her base crit damage is only 60%, crit mods are not very good for Tess.

Manifestation

M1 causes an extra Glimmerburst damage proc every 5 shots whilst Tess' ult is active.
Glimmerburst's proc is 30% ATK, so M1 averages an extra 6% ATK per shot.
This is quite a nice damage boost.
M2 causes targets to take 12% more damage for 5s after taking aptitude damage from Tess.
Also a nice damage boost.
M3 gives Tess +20% Final aptitude damage if equipped with a Frost-damage weapon (i.e. hopefully always).
A nice damage boost for Tess, but if most of your damage comes from your main-dps this may not be a large overall damage increase for your squad.
Alternatively if most of your squad's damage is coming from Tess, this can average to a large damage buff.
M4 gives Tess' Support Skill +1 level and increases its Glimmerburst damage.
As usual, this is just more damage. It doesn't change how Tess functions or how you'd play her.
M5 gives a +25% ballistic damage buff to operatives who have an aptitude buff from Tess, including herself.
This is a nice ballistic damage buff.

As usual, if you want efficiency (good damage without massive investment), then M3 is a good stopping point.

Good Teammates for Tess - Phantasia

Tess adds Frost-damage to each shot.
As such, she is only useful to support operatives that actually shoot things.
Since all Tess does is add damage to shots, the more shots an operative deals, the more damage Tess will add for them.

As such, a list of dps operatives that Tess works well with is basically just a list of dps operatives sorted by their Rate-of-Fire in descending order.

Of particular note is Katya - Rhapsody - Katya and Tess were released at the same time and were designed to work together, and Katya is the best main-dps to use with Tess (Rhapsody has a RoF of 30 shots/second).

Since Tess gives extra full-squad damage to Frost-damage operatives, she is best used with Frost-damage operatives.
Similarly, since Tess adds extra damage per-shot, Phantasia and Vidya - Celestial Swan can only be used together if supporting a dps operative who deals Frost-damage only.

Lastly, note that Phantasia does deal much higher damage than the previously-released support operatives, and Tess will out-damage all 4* operatives.
As such, Tess should never be used to support a 4* operative - you're always better off just using Tess herself to deal damage.
If you did want to have a 4* operative support Tess, then her best option is Fritia - Little Sunshine, who herself gives a thermal aptitude effect, which is good as when used as a main dps Tess spends almost all of her time in combat shooting things.
Despite this, Tess can use her ult to support herself if played solo, whereas if she is paired with a 4* she can't use her ult to support herself, as using her ult will swap her out.
As such, if you only have Tess as your only decent dps, I recommend using her solo if you can, and only support her with a 4* if she needs the healing that the 4* provides.
Phantasia + Fritia - Little Sunshine deals less damage than Tess does on her own.