Yeah, if you don't have a "real" green screen, you can probably shoot a video from the same angle where you come in from one side and stay on that side. Then use OBS's crop filter and keep your live video on the other side.

I just said to hell with it and bought a bright green sheet early on last year since I was spending so much time in meetings and assisting professors with running their classes. That sheet and a couple of cheap clamp lights (plus a decent tabletop mic) made a huge difference in the quality and entertainment value of my telepresence work.