Good news actually, it's already being worked on. As mentioned, Pipewire is the current leading solution. Upstream WebRTC has experimental support for Pipewire; in Chromium it can be enabled with a flag and in Firefox it can be enabled with a patch or configuration flag (I believe it is supposedly merged, but not sure if stable versions will compile and work with it.)
GitHub is down atm but there's also an xdg-desktop-portal implementation for wlroots which should allow for Pipewire clients to run under Sway (I have not tried this personally, so I have no idea if it actually all works in practice yet.)
https://github.com/emersion/xdg-desktop-portal-wlr