Acrobat 2024: How to control the “fill in form fields”?

This is a misleading name for that tool. You're not filling in form fields, actually, but entering text as comments.

If the file has form fields then you don't need to use any tool to fill them in. Just click them and enter text or make a selection. If it doesn't (which is what I suspect is the case with this file) then you will need to add the various commenting tool to input your text, but that is much less handy.