If you haven't just used OBS you definitely should check it out. It's an incredible piece of software. I can screen cap multiple browsers and get a webcam feed and be at ~4% CPU usage. To put that in perspective I just made an app with OpenFrameworks (C++) that just gets my camera and it uses ~6% of my CPU. OBS is amazing.
As a counter anecdote - my 2015 MacBook Pro stutters within 30-40 seconds of OBS streaming a 1080p feed to YouTube. Is there anything to tweak? Or is my machine too old?
Even a first-gen Raspberry Pi 1 is able to encode 1080p30fps video with its hardware encoder.