In Fedora and with standard desktop spins, it should work out of the box by default, in Firefox.

For Chrome, you need to enable chrome://flags/#enable-webrtc-pipewire-capturer

For more details, what packages need to be installed and what setup done (for sway, for example) see https://wiki.archlinux.org/title/PipeWire#WebRTC_screen_shar... (yes, arch wiki, the principles are same for all distros).