I love Firefox's picture-in-picture mode for this exact reason. I think there is an extension for Chrome also.
First to trigger the Javascript context menu, and again to trigger the native one which will have the "Picture in picture" option. And there are actually two different native context menus, so if the PiP one doesn't pop up, you might have to try multiple times.
Very weird UX instead of just giving us a PiP button under the video.