Shortcut to pin / unpin individual floating chat windows

By default it seems all floating chat windows are pinned by default (appear on top). I actually think I'd want the default to be unpinned, but I'd be happy with a shortcut.

I think this should be separate from the pinning / unpinning of the Quick Prompt window

Bonus: I'd like to see my floating windows in my CMD+Tab list of applications / windows.