Haru - Raikou

If you want to try her out, Raikou is available as a trial operative in story chapter SP7 - Beyond Elysium (Main Story // Journey - Allies Revisited // Beyond Elysium)

Raikou can deliver very consistent damage over a potentially very large area, with theoretically good mobility, and some self-healing, but her dps is very low compared to the other modern 5* operatives, she is slow to deal damage which can make her extremely poor against mobile enemies, she requires being near enemies which can lead to poor survivability, she can feel extremely clunky to play, and needing to see your own visual effects can make her difficult to use against enemies that spam visual effects a lot.

Note that Raikou roughly translates to "God of Thunder" in Japanese, but Haru - Raikou deals Chaos-damage, not Electric-damage.

The Basics

Role: Main DPS
Deals Chaos Damage
Weapon Type: Assault Rifle
Deals entirely skill dmg
Mobility is... mixed
She can move a lot... but she needs to stay very close to enemies

How to use Haru - Raikou

If Haru has enough U-Energy to use her ult:
Hold her ult to slash in a line and create a special trail in front of and behind her
Tap her standard skill to move to one side of her ults trail
Repeatedly tap her ult to slash on either side of the enemy.
This makes triangles with the trail from her ult, which explode to deal damage

If the special trail from her ult isn't active:

Tap her Standard Skill to dash forward and leave a trail behind Haru
or
Tap her ultimate skill to slash and leave a trail in front of Haru
(They deal the same damage, so use whichever you prefer.)
Repeat step.1 three times to form a closed loop/triangle of trails around the enemy
Once formed, the triangle will explode.
After exploding, its trails will disappear.
After forming/detonating 6 triangles, the 6th won't disappear.
Hold Haru's standard skill to detonate the 6th for extra damage.

Repeat

Note that you can create non-triangles, but Haru's dps does go down the more trails are part of the closed loop.
With her Auctus Drive #2, anything up to 8 trails is a small dps loss.
More than 8 trails is always a large dps loss.
3 trails is always the ideal amount. Any more will always cost you dps.

How to build Haru - Raikou

Weapon: Thunderlaw
Weapon Parts: Max ATK
Logistics Squad: Aozora
+10.0% ATK
+106 Alignment Index
+8.5% Chaos Damage
Best supports:
Vidya - Celestial Swan
Marian - Riptide

Specifics:

Standard and Ultimate Skill

Haru's standard skill causes Haru to charge forward, dealing Chaos damage and leaving a trail behind her.
Tapping Haru's ultimate skill causes Haru to slash forwards, leaving a trail in front of her, without Haru moving.
These both deal the same damage and the trails from both last for the same amount of time (10s), so it doesn't matter which one you use to create a trail.

When Haru's trails combine to form a closed loop/area, then the entire area will detonate for Chaos damage, removing the trails.
When it detonates, Haru gains 1 stack of "Thundercloud".

When Haru gains 6 stacks of Thundercloud she loses all stacks and instead gains "Thunder Overload", during which the light trail area no longer auto-detonates, and slows enemies within the area, and you can hold Haru's standard skill to deal Chaos damage to up to 10 targets within the area. This detonation removes Thunder Overload.
Haru's Thundercloud charge is indicated by the small bar above the ammo counter in the bottom-left.
(Basically just hold Haru's Standard Skill after every 6th closed area.)

Low-HP enemies within a closed area who are damaged by its detonation and have no shield are automatically killed.
As usual for such auto-kill effects, the HP-threshold for them triggering is so low it's basically useless.

Raikou's standard skill does have a 0.3s cooldown, so it's very spammable, but has an S-Energy cost of 5, so spamming it will quickly deplete Raikou's S-Energy.
With her first Auctus Drive, she recovers 50 S-Energy after creating a closed area, so she'll never have to worry about S-Energy once she gets her first Auctus Drive.
Without her A1 though Raikou can run out of S-Energy extremely quickly.
The Neuronic buff that reduces it to 3 S-Energy does help, but she'll still eventually run out.

When Raikou has at least 50 U-Energy, you can hold her ultimate skill to have Haru do a long slash that deals Chaos damage.
This does slash both in front and behind Haru, and the range is very high.
This does count as a trail, and can connect the other trails. This trail lasts 20s instead of the usual 10s.

Haru's ult reduces the cooldown of her ultimate to 0 for 20s.
This allows you to do the ult slash, dodge to the other side of the enemy, then spam slashes with Raikou's ult to either side of the enemy to repeatedly create areas around them.
With its first Neuronic, Haru also gains +30% ATK during this 20s, which is a good damage buff.

With its second Neuronic effect, a standard skill area detonation that includes the trail from her ult ignores 20% Chaos Resistance, which is a great damage buff.

With the infinite sustain that comes from her first Auctus Drive buff, Haru will never need to shoot anything.
Since her standard skill doesn't generate any U-Energy, Haru will never generate any U-Energy, and hence won't ever get enough U-Energy to use her ultimate unless you have a support operative who can generate U-Energy for Haru.
Haru's 5* weapon does give her one free ult every 100s, but beyond that you'll probably never have the U-Energy to use her ult otherwise.

Support Skill

Haru deals Chaos AoE damage, hitting up to 5 targets 9 times.

Like all main-dps operatives, Haru is not a good support operative, and you really don't want to use her as one.

With its first Neuronic, this can auto-kill unshielded targets that are on low HP, but as usual the HP-threshold is so low it's basically useless.

With its second Neuronic, Haru recovers 1 S-Energy and has her support skills cooldown reduced by 1s each time you defeat an enemy with any operative.
This does allow Haru to act as a sub-dps to some extent, dealing damage and then retreating to the bench once her S-Eneryg runs out to let it recover.
In practice, if you have another capable DPS, then you're better off taking another support for them, not using Haru as a Sub-DPS for them.
Alternatively, just take another support for Raikou, rather than having another dps sit on the bench doing nothing.

Weapon

Thunderlaw
Raikou's best weapon.
+18/30% Chaos damage.
Reduces the U-Energy for her next ult to 0 after detonating her standard skill. This has a 100s cd so it's effect on your dps isn't great, but it is still decent.
This does allow you an easy ult once per mission though, which is pretty nice.
+30/50% ATK and enemies taking 12/20% increased skill damage after she creates an area with her standard skill.

Interestingly, Raikou is the second 5* operative to not get a designated 4* (i.e. Pink) weapon (after Nita - Pulse - the only other Auctus Drive operative as of Raikou's release.)
As such, if you don't have her 5*, then just use whatever other Chaos AR you have.
The game recommends Ashen Dog - the 3* AR that just gives +Chaos DMG. It's fine.

The 4* AR's like Web Snare and Indicator don't benefit Raikou any more than the 3* as she can't use their effects, so Ashen Dog is generally her best weapon as Raikou can actually use its effect, and the other effects of the weapon (RoF, magazine capacity, reload speed, etc.) don't matter as Raikou is a pure-skill dps who never actually shoots things.

With that being said, Raikou's 5* weapon was given away for free during her release, so if you have Raikou then chances are you also have her 5* weapon as well.

For weapon parts Raikou wants maximum ATK.

Logistics

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

This gives Raikou +45% Skill DMG whenever a closed area is present.
For each trail, the area detonation damage increases by 15%, up to 3x (so 45% Max), which includes those trails forming an area.
... so basically just play Raikou normally by forming areas from at least 3 trails and you'll max out the damage bonus from her logistics squad.

(As yes, her skills do technically deal damage with a closed area, and then the closed area disappears, so the trails do buff themselves.)

For stats, Haru wants +10.0% ATK and +106 Alignment Index
For the special stat, Haru wants +8.5% Chaos Damage.

ATK and chaos damage for more damage.

+106 Alignment Index gives Haru another +5.3% ATK.
This is not the best bonus, but Haru doesn't really benefit from most other stats.

If you don't have her first Auctus Drive, then S-Energy Recovery is also a very good cope stat as it allows her to spam her standard skill much more.
Once you have her first Auctus Drive though S-Energy Recovery becomes useless, so you're better off just going for Alignment instead so you don't need to re-roll later.

Auctus Drive (I.e. her Manifestations)

With A1, whenever she creates an area with her standard skill, Haru resets the cooldown of her ult, gains 50 S-Energy, and recovers 5% of her Max HP.
This is an ok amount of healing, but does average a few percent per second at-best, so it won't save you against strong or highly sustained damage.
Resetting the cooldown of her ult isn't overly useful, as the limitation to how often you can cast her ult is its U-Energy cost, not its cooldown.
For tapping her ult, you still can't from a triangle just using her ult, so it doesn't change how you play Haru - you still need to dash with her standard skill.
Recovering 50 S-Energy though is a huge change though, as it allows Haru to just keep spamming her standard skill indefinitely.
A2 causes her standard skill detonations to deal more damage the more trails above 3 it consists of, up to a max of 8 trails.
Each trail above 3 gives +30% Final detonation DMG, so 8 trails would give +150% Detonation DMG.
Trails 3-8 will give 100%, 130%, 160%, 190%, 220%, and 250%, respectively.
This is 0.333%, 0.325%, 0.32%, 0.3166%, 0.3142%, and 0.3125% damage-per-trail.
The most efficient (i.e. highest-dps) way of dealing damage is still 3 trails, but you don't lose much by going with more trails [up to 8].
As such, you won't actually want to use more trails, but if you mess up your aiming and need extra trails to form an area then with A2 you at least won't lose much damage.
A3 causes Haru's standard skill to reduce the cooldown of her ult by 1s, and whilst under the 20s state of her ult, her standard skill dashes farther.
This can allow her to make a larger area without requiring more dashes, potentially increasing her AoE.
This also allows her to ult, dash farther off to one side, then spam her ultimate skill as usual - but the increased dash distance may be useful there.
This is an ok QoL buff, but doesn't necessarily increase her damage at all.
With A4, Haru's standard skill detonation deals more damage the fewer targets there are within it.
8% final detonation DMG per target below 5 is quite a large damage bonus against single-targets.

Being an Auctus Drive operative, you'll generally have Raikou at either A0 or A4.

If using Raikou to create the [optimal] 3-dash standard skill AoEs against a group of enemies, then her Auctus Drives improve her QoL and sustain, but does not necessarily increase her damage at all.
Her Auctus Drive buffs do give her an ok single-target increase of 40%, but compared to the actual Manifestations of other 5* operatives the damage buffs of Raikou's Auctus Drive upgrades are small.

Good Supports for Haru - Raikou

Raikou deals Chaos skill damage exclusively.
As such, she has two ideal supports:

Vidya - Celestial Swan for the resistance and DEF shredding
If using Celestial Swan, make sure the other support isn't off element to Raikou.
Marian- Riptide for the skill damage buffs.
Raikou's very frequent skill casts will charge up Riptide's Tidesong very quickly, allowing Marian to swap in frequently for high damage.
Riptide is on-element to Raikou, and hence works with Celestial Swan.

Other skill-damage buffers or resistance debuffers are also good, but Celestial Swan and Riptide are Raikou's best supports.

Siris - Freefin's Skill-DMG buffs are still great
Freefin is off-element to Raikou, but since Raikou can maintain Siris' buffs, this isn't an issue - just cast Siris' support skill before Haru starts using her skills.
Eatchel - The Cub's ATK buffs are still good
Raikou can actually heal herself, so Eatchel's healing is less useful for Haru than most other operatives.
Mauxir - Shadow Ka still works well for giving an extra target for Raikou to hit.
Shadow Ka is on-element to Raikou.
Chenxing - The Observer
Chenxing's skill-dmg buffs are still useful, but you'll need to position her support skill carefully so Haru can dash around it and stay within its PBAoE.
It may not always be possible for Haru to stay within Chenxing's PBAoE, which makes Chenxing somewhat inconsistent.
The extra AoE Chenxing gets from her M5 is very useful for Haru, as it makes it much easier to stay within Chenxing's support skills PBAoE.