Have you ever thought of giving her a Soul Society au where she is enlisted in the Gotei 13? Would she betray the Soul Society with her dad or not?
I'd give her a soul society au but I genuinely cannot find a motivation for her outside of Sosuke's dictation.
One version I thought of:
I had one written where she was actually raised by her mother. But Akari is still carrying Sosukes traits. She kills her mother to enter the Soul Society solely so she can survive. Even without Aizens influence, she still carries psychopathic & antisocial traits. Where Sosuke psychologically picked her apart & manipulated her to connect to him through fear & desire to appease, Akari dies not have the ability to connect to others. She would also find it hard to communicate. Her mother only taught her latin since she was sheltered. So she feels more disconnect
Even without Sosuke, she's naturally lonely & apathic toward people. She killed her own mother, who did her best to keep her alive but feared her power & judgment of others. Akari saw that as a weakness. In that version, I don't see her having any reason to join the Gotei 13 other than to be fed since that was her struggle. She only cares about herself & lives for herself. She may know Aizens, her father, bc her mom said his name, but she doesn't care about it. After being raised by a posessive, overbearing mother, she doesn't want another person on her ass.
Basically a literal - less smart baby Aizen.
It's pretty much the same for her canon but she's in the Soul Society. In this version he doesn't put her through Hollowification immediately ( which is why he didn't put her in there in the first place). She's still reclusive & aloof without regard for others. BUT she was taught to mask it. She's just not good at acting so she just smiles & nods. She gets arrested after Karakura since she does survive for her betrayal & imprisoned. Perhaps fed to the war but she'd be put back in prison
Either way...it doesn’t change her character much unless she was raised by her mom. She gets those traits from her father, & some by her mom who was narcissistic & posessive but she did love Akari. despite being loved by her mom, she still turns on her.