Having an overlay-type feature that I can see no matter what

Kinda like how you have the overlay when playing games, except I want one when I'm browsing the web, doing work, or even just on my desktop. The mobile version of discord has this and it would be awesome if the desktop version had it as well.

It would also be cool if you can move the overlay where ever you want, kinda like how you can do that with chat heads on Facebook messenger mobile.