Chenxing - The Observer is a 4* operative, and is thus not worth wasting logistics re-rolls on - you should save your re-rolls for your 5* operatives.
Chenxing works well as a dps and also as a skill-damage/healing support, however there are other 4* operatives that deal similar damage to Chenxing, but Chenxing is one of the best 4* support operatives.
Since Chenxing's Support Skill doesn't deal any damage, there aren't really any logistics squads that work well for her as both a dps and a support, so you should generally try to build Chenxing as a support rather than a dps.
WIth that being said, one you start getting 5* operatives you'll stop using Chenxing anyway, so it doesn't really matter how you build her.
Once you get good 5* supports, you'll never use Chenxing as a support, however it's possible you might want to use Chenxing as a [weak] dps, just for some variety, so building her as a dps is fine.
Overall I recommend you aim to build Chenxing as a support, but if you have enough 5* operatives that you never use Chenxing as a support, she's likely better off being built as a dps.
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 with Chenxing.
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:
Neither is particularly good, but they're the only squads that actually provide her any real benefit.
I'd generally recommend Xinye, but Lux does work fine.
For stats Chenxing wants +10.0% ATK and at least one +19.3 Skill Haste roll.
For the Special talent, Chenxing wants +8.5% Electrical Damage if using her as a dps, and +10.6% Healing Bonus is a good stat as a support.
Chenxing does so little healing that giving her Healing Bonus doesn't affect her that much
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 a full 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.
As a DPS, Chenxing deals damage with both her Assault Rifle (which deals ballistic damage) and via her turrets (which deal skill damage), however most of her damage comes from her gun, meaning that Chenxing generally wants ballistic buffs, however buffing Chenxing's ATK will buff all of her damage, as that buffs her turrets too.
For dps, Chenxing's best logistics squad are Amano-Iwato, which massively increases her ADS ballistic damage, and Twilight, which debuffs enemies resistance.
Mingyi also performs very well, and is the easiest to use, as it doesn't require her to use her Standard Skill turrets or aim at the enemies weakspot.
Good squads for her include:
Amano-Iwato
Increases ADS Ballistic DMG by 10% after a crit. Max 5 Stacks.
The 2-piece also gives her Ballistic damage, which is very useful.
Since Chenxing has nothing that guarantees a crit, if using Amano-Iwato then she'll need to aim at the enemies weakspot, as weakspot hits always crit.
A great choice if you are ADS'ing with Chenxing.
If you only hipfire and don't ADS then it's obviously terrible.
Twilight
After dealing DMG with an Active Skill or Auxiliary Unit, the target's Resistance to that type of DMG decreases by 16% for 5 sec.
Chenxing can proc this using the drop pods from her Standard Skill, reducing the enemies Electrical Res, which makes it a very passive way of increasing all her damage.
Mingyi
When dealing Electrical DMG, increases ATK of the equipping operative by 1% for 3 sec. Max 45 stacks. Repeated triggers will reset the duration.
Still less total damage increase than Amano-Iwato, but again - doesn't need ADS, and you can still stop part-way through magdumping to use a skill, which is nice.
If using Mingyi, then Chenxing will need to have an Electrical-damage weapon equipped.
Mizuho
When shooting continuously, each shot increases Ballistic DMG by 3%. Max 20 stacks.
Chenxing's decent magazine capacity allows you to get a good average damage bonus from this (14.5% on average)
Mizuho gives less damage than Amano-Iwato, but you don't need to ADS to get it, although you do need to fully deplete the magazine in one go without stopping.
Given Chenxing's long skill cooldowns, this will happen most of the time anyway.
Mizuho isn't a great squad for her, but since Chenxing is only a 4* operative it might not be worth the Presence needed to get her a logistics squad, and if you have Mizuho already it will work fine whilst saving you some investment that could be going towards your 5* operatives.
Note that Chenxing's turrets from her Standard Skill are Aux Units, and hence do not proc Thebes squad, so that is not a good choice.
Her turrets will benefit from Aux Unit buffs, such as from Usha squad, however Chenxing out-damages her turrets by so much that you shouldn't give her Aux Buffs - you're much better off buffing Chenxing and not her turrets.
For stats Chenxing wants +10.0% ATK and +10.6% Crit DMG Amplifier.
For the Special talent, Chenxing wants +8.5% Electrical Damage.
If giving her Crit DMG Amplifier, make sure you always shoot the enemies weakspot, as weakspot hits always crit.
If you aren't going to aim at an enemies weakspot, then her 2nd stat doesn't really matter - nothing particularly buffs her dps.
Crit DMG Amplifier is still likely her 2nd best stat even then though.
Alignment Index only boosts her U-Energy Recovery, which isn't that useful for her dps.