Not Linux, and not exactly what you're asking for, but Windows PowerToys has VideoConference mute which seems to install an audio driver that can globally mute. Not sure if something like this exists for Linux.
It's easy to globally mute on Linux, but that doesn't show the "you are muted" UI elements, and makes the UX a bit more confusing. I wanted something more explicit, which is hard.
https://docs.microsoft.com/en-us/windows/powertoys/video-con...