I agree — you should be able to limit the dot to one display, or to displays that have a menu bar, or something like that.
But, you were asking about better privacy than before Monterey? Which, yeah, it's better. Not by a huge margin, but better.
Ah, I missed that one. I basically was reacting with another post (before yours) in mind from someone who still persists in complaining about his/her security. Sorry for the clutter.