Chenxing - The Observer

If you don't have her yet but want to try her out, she is available as a Trial Operative in Story Mission 9-12

The Observer is a highly versatile 4* operative - she has good damage and mobility, and can heal and support allies too.

Whilst she is one of the best early-game healers, you only ever need 2 healers, and Chenxing's healing being massively outclassed by both Eatchel - The Cub and Yao - Quiet Quitter means that Chenxing generally won't be needed as a healer once you've unlocked Eatchel.

Chenxing can buff allies skill damage once she has her Manifestation 1 and 3, which stacks with the standard skill damage buff from her Neuronic, meaning Chenxing's support skill is good at buffing allies skill damage, and Chenxing is the games best 4* support for other operatives who deal skill damage.
Her main limitation is that she's only a 4*, and her dps and support capabilities are low compared to the 5* operatives, and that without her Manifestations she is a much less effective support, and by the time you've gotten her Manifestations to buff her support capabilities you'll probably have 5* support operatives who will completely outclass her.

By 5* standards The Observer is not a great operative, but she is a great 4* operative.

The Basics

Role:
Early-mid game: Main DPS
Late-end game: Skill-damage support/healer
Deals Electric Damage
Deals both ballistic and skill damage
Mobility is decent

How to use Chenxing - The Observer

As a DPS:
1. If her ult is available, use it
2. Spam her standard skill off-cooldown
3. Otherwise, just shoot stuff.

As a support:
Spam her support skill as often as you can.

How to build Chenxing - The Observer

Weapon: Trial's Eve
As a support Strawberry Shortcake is also fine
Weapon Parts: Max ATK
Logistics Squad: Xinye or Lux
+10.0% ATK
+8.5% Electric Damage
Best squadmates:
With Chenxing as a DPS:
Fritia - Little Sunshine
With Chenxing as a support:
Acacia - [Redacted]
Marian - Queen of Pain
(Chenxing and Marian both buff Acacia)

Standard Skill
Chenxing slams down a "drop pod" (although "turret" is a better word) in front of her.
After a delay, this transforms into a "Thunder Soldier" which deals electrical damage to the nearest enemy that chains to up to 2 extra targets.
With her Neuronic buff, it also deals a chaining Electrical damage attack whenever it attacks. This deals more damage the more Thunder Soldiers you have.
This is actually very strong.

Chenxing can have up to a max of 3 of these Thunder Soldiers active at a time.
Chenxing can summon 1 Thunder Soldier every 10s, and each lasts 30s.

With her Neuronic, Chenxing being near a Thunder Soldier recovers some HP for the Thunder Soldier and increases its duration by 1s.
This gives the Thunder Soldiers unlimited duration as long as Chenxing stays near enough to keep applying the Neuronic.
Chenxing still has extremely high uptime without the Neuronic buff, so it's not actually a significant buff for uptime, but not having to cast as often is nice.
The healing is extremely weak (5% of max HP), and isn't really enough to keep them alive in a fight where they are taking any form of damage.
They can be healed by Eatchel's passive healing though, which increases their survivability dramatically.
Whilst the Neuronic does allow Chenxings Thunder Soldiers to have unlimited duration, their low base HP means that they are often just one-shot by endgame foes.
That they are immobile also means they tend to take a lot of damage, as they can't strafe or move out of the way of enemies like a player can.
Similarly, Chenxing wanting to stay near them to apply her Neuronic buff also makes them take a lot of damage from the AoEs aimed at Chenxing.
This mean that staying near them to extend their duration can often result in them dying very quickly.
Your best bet is sometimes to just cast them and then stay away from them so they don't take any damage, and just resummon them as needed.

These Thunder Soldiers deal 18% ATK every 2.5s, for 7.2% ATK per second dps, or 21.6% if you have 3 up, which is not great by modern 5* standards, but being largely passive does allow Chenxing to shoot more and cast skills less, which is a plus, and being able to spend most of her time in combat shooting enemies does add up to give Chenxing quite high overall damage for a 4* operative.

Support Skill
Chenxing slams down a drop pod in front of you.
After a delay, this transforms into a "Purity Mark" that drops an item that restores some HP every 5 seconds.
(This is technically Chenxing's healing, not the Purity Mark, so it's unaffected by Auxiliary Unit buffs.)

Since this heals at the start and every 5s, and lasts 15s, and each pulse only heals 6% of Chenxings Max HP, the total healing isn't massive (24%), but it is something.

With her Neuronic, being healed also gives +10% Standard Skill DMG for 3s.
Since one is thrown out every 5s, this is 60% uptime for the buffs duration (which is itself 75%), for 50% total uptime.

With her M2, the rate that Purity Marks are thrown out is decreased to 3s, meaning her 10% Standard Skill DMG buff has 100% uptime for the support skills entire duration.

Ultimate Skill
Chenxing drops a "Thunder Token" (basically a "drop pod"...) in front of her which gives a massive attack speed boost to the Thunder Soldiers from her standard skill.
A 150% attack speed increase is huge, but obviously buffing her Thunder Soldiers is only useful if she actually has any Thunder Soldiers to buff.

With her Neuronic, it also deals PBAoE Electrical Damage upon creation.

With her other Neuronic, Chenxing herself can chain the chaining Electrical damage attack from her standard skills Neuronic buff, increasing its damage.

Weapon

As a support: Strawberry Shortcake*
This gives an ATK buff to the deployed operative when the equipping operative uses her support skill.
Given that Chenxing works very well as a support operative, Strawberry Shortcake is generally her best weapon.
The buff from Strawberry Shortcake lasts 15s, which is the same as the cd of her Support Skill at M1, allowing for 100% uptime on Strawberry Shortcake's buff.
As a DPS: Trial's Eve*
This has high base damage, is on-element, and gives a nice ATK buff after any team member is healed, which Chenxing can maintain with her support skill without any Skill Haste buffs.
This is Chenxing's highest damage option as a DPS, but Trials' Eve does only apply a 20% ATK buff, whereas Strawberry Shortcake provides a 22% ATK buff, although Strawberry Shortcake does need some Skill Haste buffs to get 100% uptime, whereas Trial's Eve has 100% uptime without any Skill Haste.
Trial's Eve deals Electrical damage, and thus does proc Chenxing's M5 bonus to increase her buffs AoE radius by 50%.
Trial's Eve does also give Chenxing an HP buff, which does therefore buff the amount of healing she does, which is useful.

Trial's Eve is technically slightly worse than Strawberry Shortcake when using Chenxing as a support to buff your damage, but Trial's Eve not needing Skill Haste and working with her M5 bonus makes it generally easier to use.

Overall, I'd recommend you give Chenxing Trial's Eve if you have it, and only give her Strawberry Shortcake if you don't have a Trial's Eve to give her, however Strawberry Shortcake is perfectly vialbe, and the difference is tiny.

Logistics

Since her support skill doesn't deal damage or inflict any control effects, many of the common logistics squads used by support operatives don't work overly well.
For example Twilight doesn't work because her support skill doesn't deal damage, and Amarna doesn't synergize because she's a skill buffer but Amarna buffs ballistic damage.

Squads that work:

Xinye
Gives extra U-Energy recovery and recovers U-Energy after using her ult.
Lux
Extra healing

Neither is particularly good, but they're the only squad that actually provide her any real benefit.
I'd generally recommend Xinye, but Lux does work fine.

For stats you want +10.0% ATK and at least one +19.3 Skill Haste roll.
For the Special talent, you want +8.5% Electrical Damage if using her as a dps, and Healing Bonus is a good stat as a support.

Skill Haste decreases the cooldown of Chenxing's Support Skill, which is useful to maintain 100% uptime on its buffs.
The buffs from her support skill last 18s after she gets M2, so one +19.3 Skill Haste roll is enough to have 100% uptime on her damage buffs.
From there you will want one S-Energy recovery mod to help sustain her high S-Energy usage.
For the last roll either another Skill Haste roll to get her cooldown to below 15 seconds, which is useful for Strawberry Shortcake, or a second S-Energy roll to help with sustain.
Which is better depends on how long fights will last and whether you are using Trial's Eve or Strawberry Shortcake.

Manifestation

M1 gives her standard skill and support skill a 15% Skill DMG PBAoE buff.
This is actually quite good, and makes Chenxing one of the easiest-to-use skill dmg buffers.
Chenxing also has high uptime on her drop pods, which thus gives this M1 buff good uptime as well.
M2 increases the rate at which Purity Marks are thrown out by her support skill from 5s to 3s.
This allows her 10% Standard Skill DMG buff to have 100% uptime for the entire duration of her support skill.
M3 gives the buff from her M1 and extra 15% Skill DMG buff after staying in its AoE for 3s.
This means Chenxing provides 30% Skill DMG, as well as the 10% Standard Skill DMG buff from her support skill as well, making her a very good support.
M4 gives her support skill +1 level, as well as reducing its S-Energy cost to 38.
Note that M4 itself says "38%", but that's wrong - All operatives by-default have 50 max S-Energy, so 38% would be 19 S-Energy.
M4 reduces the S-Energy cost to 38, not to 19.
M5 gives her M1/M3s buff +50% AoE when Chenxing has an Electrical Weapon.

Being a 4* operative, you'll get all her manifestations eventually.

Good Teammates for Chenxing - The Observer

As a healer, Chenxing can support all operatives, although she isn't as good as Eatchel - The Cub or Quiet Quitter, but she is a good early/mid-game healer before you get Eatchel.

As a support, Chenxing provides skill damage buffs and standard skill damage buffs, and as such she is a good support operative for all skill damage operatives.
She's not as strong as many 5* skill damage buffers, such as Riptide or Freefin, but Chenxing is still good, especially for a 4*.

As a main dps, Chenxing deals both ballistic and skill damage, and as such works best with universal supports such as Vidya - Celestial Swan and Eatchel - The Cub.
Since she spends most of her time in combat shooting stuff, ballistic and per-shot aptitude buffs such as Phantasia, Little Sunshine, or Starshine all work well with her.
Generally speaking though, since most 5* operatives will out-damage The Observer, you should just use her as a support for your 5* operatives, or support her with whatever 4* operatgives you have.

For 4* operatives, The Observer pairs well with Acacia - [Redacted] - Chenxing provides skill damage buffs that Acacia can make good use of for her skill damage, with Acacia dealing good damage against groups, whereas Chenxing deals better single-target damage, and you can swap between Chenxing and Acacia depending on whether you need Single-Target or group damage.