Do both the sharing and receiving users need to install the app? If not, it would probably be much easier to start using the app if at least the receiving user could view my screen from their web browser.
Apart from that, I often fall back to https://github.com/adamyordan/laplace when I need to share my screen. It works in the browser and has great image clarity. Sadly, the demo instance is down, so you need to host it yourself. Also, it can have trouble inside some enterprise network/firewall setups.
With WebRTC the "without any server infrastructure" only refers to the P2P part. The session initiation is outside of this. So in practice this means you need a server for the initial handshakes and then the actual session is P2P.
Running over WebRTC the web browser based person can communicate with the host person who is running a native WebRTC app.
The session initialization needs some kind of middle man (server) that lets both parties to agree on the session communication details. This per se doesn't really need any account.
The person who wants to host the session could generate a temporary one time auth token that they then communicate to their peer using whatever means (send a pigeon, use email, chat app) that lets the client to connect to their host.
Sure, but somebody will have to host the website for the "web browser based person"? Even though the audio/video traffic will be P2P, there has to be some interface in the browser?
I keep wondering whether this browser interface would be possible on a static website with all code running client-side.
That is totally possible if you just want to join a driver/host.
If you want to take over and become the driver that would not be possible or with some real limitations (not being able to give access to your keyboard/mouse and also not having the ability to show the cursors of the participants)
Apart from that, I often fall back to https://github.com/adamyordan/laplace when I need to share my screen. It works in the browser and has great image clarity. Sadly, the demo instance is down, so you need to host it yourself. Also, it can have trouble inside some enterprise network/firewall setups.