I also just realized that if I place my laptop camera in the exact same spot, while recording the background video and during class, all I need to do is sit on the left of the camera pane during class, and only stay on the right for the background video, then I just need to stitch the two videos side-by-side in OBS and it should work well enough.

I think I achieved my purpose here. Ask a question from a bunch of smart people. Either they give a great answer, or their response forces you to rethink and figure out a simple solution. Thank you HN for being my AI enabled rubber duck.