I'd like to have a solution where chroma keying is done in hardware and ideally also something where I can combine my monitor picture and my camera to do "talking head" videos without software running on my main laptop. It should "just" receive the final picture ready to be streamed to Zoom et. al.

I'm probably not explaining very well. In the end I want to rely on OS & Software as little as possible because things keep breaking (on Linux) for me so if I can just get a single video feed to select as the camera source for Zoom, Teams et. al that'd be great.