@notbugs Which controller are you using? Or do you have any controller hooked up at the moment? Last time this happened to me, my PC automatically switched the audio input to go through my controller. Might be worth to check that if that's the same case as yours.
I'm actually surprised you're able to get it working with Microsoft Edge, since I believe Chromium based browsers aren't supported.
To add on to this - I encountered the same issues (and more). The issues I had were:
1) No audio, despite audio performing fine elsewhere (and chrome was verified to NOT be muted).
2) When starting games, the screen would stay black until I pulled up the exit screen then returned to game.
3) In some instances, the start game button (circle with play symbol inside) that overlays the game in the Stadia interface would just be a circle.
After looking at this post, I went through my plugins and discovered that my "Disable HTML5 Autoplay" plugin was causing all the issues above. After disabling this for the session, things worked beautifully.
I now realise that in my post for solutions I failed to name the plugin that caused my problems but with your reply @aeonstorm I can confirm that it was the exact same plugin that caused my problems. So one point on the checklist for troubleshooting audio issues should be to check if the "Disable HTML5 Autoplay" is installed and either uninstall it or tweak the settings for the plugin to not affect Stadia. The weird thing about my issues was that in the beginning when Stadia was new it worked just fine but at some point something happened that caused the plugin to go nuts on me. By the way I can also confirm that I had all the same issues as you mention in your post @aeonstorm. So that is another indicator that we experienced the exact same problems caused by the "Disable HTML5 Autoplay" plugin.
K. Didn't find a HTML5 plugin on my pixelbook go. BUT, did talk to tech support and audio worked like a charm in incognito mode, so they said it was definitely extensions related. Went to chrome://extensions and started turning them off one by one. Turns out my cause was Google Docs Offline. When its off, audio works. On, audio is off.
So, there's that.
Scratch that. It worked for one day. Still unable to get sound. Playing on Chrome on a Pixelbook Go. Tried bluetooth connected to compy, plugged in to the controller and plugged in to the laptop. NFG. Frustrating as funk.