Since it looks like your webcam is mounted to a stationary PC and you're only really writing this for yourself, wouldn't it be a lot easier to just subtract out a static picture of your background from the feed?
Chroma keying is the stable version of this idea: the single background color of a separately and well lit background removes these issues.
I did actually tinker with this and other approaches a little.
Also the things in the background get moved around pretty frequently, e.g. what is on the couch. I don't have a dedicated office room
If you have the space, and good lighting it's a much simpler approach.
It's also less fun though, and I could do this with what I had on hand pretty quickly.
Random example clip: https://youtu.be/T5uqB1Kqukw