Funnily enough, she'd be less suited to actually have Projection Sorcery (PS) narrative-wise because of said ability to use it.

A large part of the 'point' or theme of PS is the users being people who make hasty and shallow judgements of everything they perceive to then operate on - literally 'flattening' it, as you could say. And PS expands on that by requiring you to play perfectly all the time, essentially forcing you to be hasty and shallow with your judgement unless you're genuinely just that cracked.

So yes she could probably use PS quite well, but that kind of misses the point and what it represents. Cursed Techniques are based on and reflect the user, after all. PS is also one of the CTs that most obviously reflects and suits their user(s), alongside things like Limitless, Shrine, Copy, Blood Manipulation, etc.

TL;DR: she's too good to actually have PS in the first place. Also it just really doesn't suit her at all; she seems more like the opposite of a PS user the more that I think about it