And yes, she should have Soul Manipulation which is supported by her one glaring pedigree of
eating a deceased avatar of the sun . There shouldn't be any reason why it isn't on her page, which is further supported to the sun god she ate being a
divine spirit , all which have soul manipulation by default. She isn't borrowing it's power, she didn't take a portion. It is inside of her, part of her, and hers to control.
Speaking of control, it's more convenient for her to not have any. The whole reason behind the events of TouhouSA is because, and is implied,
that she has to release it occassionally, much like a reactor cooling down after building up so much heat. Can Asriel's passive paralysis hold back the force of an exploding sun?
She opens with it too, and has been shown to not need to point her control rod to do so.
One could argue from this alone that she can attack even while paralyzed. And if Azzy's paralysis is directly related to the soul, (if that even matters because of her youkai physiology, and she
cant necessarily be killed with typical magic-slinging attacks anyway. ), then she can tolerate it.
Edit: Unrelated, but she's also dumb enough to not adhere to spellcard rules.