Pipewire [0] (the successor to PulseAudio) attempts to streamline this process for
Linux. I've been messing with wf-recorder [1] for my screen+audio recordings, and
might try to get it to spoof a camera input so I can get any program attempting to
connect to the webcam to instead turn into a screen-casting tool.
[0]: https://en.wikipedia.org/wiki/PipeWire
[1]: https://github.com/ammen99/wf-recorder