This is the first time I’m seeing it used this way, I’m afraid, so I can only go off of this example and the grammar explanation provided by kanshudo. The article shared by the stackexchange answerer doesn’t want to give me anything more than the foreword of the article, for some reason. Maybe because I’m on mobile.
What I will say is that it does seem a little odd that the stackexchange link mentions it maybe being sarcasm or indifference because that doesn’t fit this scenario very well, but the kanshudo link I provided doesn’t make any mention of that. It does say it can be viewed as a contraction of っと思います, which viewed in that way fits our scene just fine:
“Then, I think I’ll ask for your help/entrust it to you/however you want to make お願い work in English.”
Aiko could also kinda be halfway-talking to herself as well, tbh, which would be more along the lines of what the first meaning of it would be (rhetorical speech, speaker convincing themselves). I do the same thing, where I’ll say a sentence out loud that could be taken as directed to somebody else, but I’m actually kinda in my own head, not really speaking directly to them, like, “Oh, I guess I can let you help” type of thing.
The reason why I float this possibility is that entire scene, Aiko-san is a bit flighty. The following line, she asks Hanabi where her glasses are when they are on her head, so it’s pretty clear she is not entirely present and is a bit out in space, so to speak, right?
Edit: also, if I take away likes randomly and regive them, forgive me. The new react system is kinda awful on mobile, and it opens up accidentally all the time while I’m just trying to scroll. I promise it’s not on purpose. -.-