Akitsu
Akitsu gives her 1 stack every time she uses her standard skill, 10 when she uses her ult, and 5 upon defeating an enemy.
At 15 stacks she gets +25% ATK for 10s.
At 30 stacks she gets +20% Kinetic DMG for 10s.
All stacks are cleared when she reaches 30.
This provides a good ATK and Kinetic DMG buff, provided she can keep spamming her skills.
Twilight
After a skill damages an enemy, Twilight reduces the targets resistance to that damage type by 16% for 5s.
Since Haru spams her standard skill a lot, Twilight is easy to maintain for her.
Thebes
Gives +2% ATK for 5s after hitting an enemy with a skill. Max 20 stacks.
Haru spams her standard skill a lot, making it easy for her to build stacks of this.
For general content where Haru will defeat enemies often, Akitsu is her best logistics squad.
Twilight is generally the most consistent, as Haru only needs to spam her standard skill to proc it, which she does a lot.
Thebes is easy to get though as it's one of the standard squads, and does work very well.
Overall I'd recommend Akitsu, but Twilight and Thebes are good options too.
For the special talent, Haru wants +8.5% Kinetic Damage
For the basic talents, Haru wants +10.0% ATK.
For the second basic talent:
Alignment Index increases the threshold of her instakill.
With three max-roll Alignment Index stats, the threshold will increase from 40% to 71.8% of Haru's ATK.
(So increasing from maybe 2,000 HP to around 3,500 HP.)
This is a decent increase, but Haru deals enough damage and can spam her standard skill enough that this doesn't really help her that much.
It does have some use against trash mobs, but with enough investment Haru doesn't really struggle too much with those.
Haru can go for Skill Haste, but with her ult active that's mostly useless.
Without her ult active, Haru can simply shoot enemies to recover S-Energy and reduce the cooldown on her standard skill, so she doesn't really need Skill Haste.
(although it does help.)
Even if you did get Skill Haste, she can start to run into S-Energy issues over very long fights if she doesn't shoot enemies much.
No second stat really helps her that much - Alignment Index and Skill Haste aren't great, but they're the best she's got.
Alignment Index makes her a bit better for regular gameplay as it helps her against trash mobs, whereas Skill Haste is a bit better against bosses.
Neither are massively useful though.
I'd probably go for Alignment Index myself, but powercreep has meant she's now a very poor choice for bosses, but Haru is still fine for mobbing.
Skill Haste is a good choice though nonetheless.