I think it would be a good ease of access and quality of life feature if you're able to right click the tab you're wanting to view in PiP. For example, you're currently watching a video in PiP but need to close it to get a full view of whatever tab / application you're currently viewing, then instead of having to go back to the tab with the video and mousing over the video player to once again enable PiP you can simply just right click the tab at the top and enable it from there.
A couple of issues I can see with this being added are:
I attached a fairly basic mock up to illustrate my suggestion.