Give us an auto-PIP option that enables PIP automatically when I change from a tab that is showing a video to another tab. When going back to the original tab and that video source is shown, disable it again.
When multiple video sources are available, make it so that the last viewed tab with a source is shown in the auto-PIP. It should also be possible to have multiple PIP instances open (like it is now) but the ones that are enabled manually should also be disabled manually.