As has been established, the crux of the issue with this Contract was a single concern regarding the Protagonist's secret; her #HiddenTruePower.
As for what that power might be, I could only assume that it was some kind of magic or other similar power that exists in this world. Of course, there was no way to confirm that for sure, so all I could do was focus on other things that may be able to give me a lead.
On that front, I tried thinking about various things for a while before I had somewhat of an epiphany. It was related to the Protagonist's behaviour.
'She shows nothing but vulnerability...'
It was a detail hard to ignore, but one I hadn't really thought too deeply into, just chalking it up to being the #NaiveProtagonist Tag.
Even in the middle of this academy, full of powerful young nobles and students of various arts like swordsmanship and magic, it would be effortless to just summon the Black Wisp from the Storage and shoot her in the head right where she stood.