Yes, it does. Like I have said, that part of the protocol is called MatrixRTC. It is not a hack, or a mod, or third party.

Matrix is a protocol, its all through some other software. Livekit is just a good and easy webrtc server that you can tie in with something like synapse

Join different servers then? Not sure what to tell you.

I use element and I am in many different matrix servers with voice rooms. I host my own as well, voice is done via livekit which makes connecting via MatrixRTC very easy, and is easy to setup and host.

Those same voice rooms support webcams / video, as well as screen sharing.

Matrix has all that these days too