Not op. But...

On Linux I set up OBS to capture my game window and from obs you are able to set the captured screen as a webcam stream.

On Linux I had to install some stuff to get a restream of the audio. It looped the game audio into a virtual mic.

So...

I Jitsi I just set my mic and video to the appropriate obs-made virtual cam and mic.

My upload maxes at 10mb/s

So I didn't have the best luck with Jitsi. Definitely not full screen quality.

But OBS might come in handy if you find another way to stream.

OBS I believe is available for windows, Linux, and Mac.