Im following matrix dev work very closely so im wondering if you have been trying the old call system (jitsi or 1:1 calls) or the new one (element call). the new one should work well for screensharing video but ofcourse you do have some level of compression artifacts. the element-desktop client should have it enabled by default since a few version ago. You can quickly test it out here without an account too call.element.io

For noise removal it just uses the standard webrtc noise filtering stack afaik which does suck, but i have it disabled and do that kind of audio filtering systemwide on my linux machine with easyeffects.