I rarely record my video but when I do I just use ffmpeg with relevant parameters.
Screen sharing is done via a ffserver as well.

The initial idea/setup is from https://blog.z3bra.org/2016/08/desktop-streaming.html but I found a ton of other scripts and configs all around github and the internet that I incorporated.

I would use OBS-Studio if I were to use a more flexible and customizable system.