Sorry for the ugly example, but it would be the idea...
- Same dual logic as the mute/unmute => pip/unpip
- visible only if a pipable content is detected (like audio and mute/unmute button)
- click on tab without running PiP, opens the PiP
- click on tab with running PiP, closes the PiP + stops the playing
- shift+click on tab with running PiP, closes the PiP, does not stop the playing,