Theory: Aoi already knows a lot and has her own agenda
A comment on the most recent chapter about how Aoi might have been awake dunring Yodaka's monologue made me think that she's not the damsel in distress she was made to look as.
I'm starting to think it's a ruse to divert attention as she attempts to find the truth about her family. She pretends to be a klutz and does it so well nobody suspects she knows there are ninjas all around her, all of whom are also fabricated personas. It's possible that she caught it at some point.
The Mukai used to be an influential family that failed to produce ninja (whatever that means) but their blood was still a powerful asset. Not only that but Kawasemi claims to be her brother, for some reason. It could mean that the rest of the Mukai are still around, living in secrecy.
She barely questions the fact that she goes unconscious whenever something secret happens nearby in order to not raise suspicion. I'm not even sure she's actually unconcious. Yodaka might be a battle genius that can adapt to pretty much any situation, but he might not be the only one. What if she's the one using Yodaka to acquire more information about herself?
The authors previous work had a female protagonist and it's clear they like giving the women the spotlight. It would be strange to make the female lead such a cardboard "happy-go-lucky schoolgirl" personality. She will likely have her own emotional arcs and development as a character and it could be a pivotal moment for the series as a whole.
In conclusion: Aoi is the Shinobi Undercover