Sorry for misinterpreting your role here on the forums, it just looked to me like you were the only person on here attempting to solve the problems of the users/devs, so I assumed you work for twitch.
Thanks for the example. On Win10 Firefox 78 and Chrome 84 it unfortunately does not work for me.
For Chrome it starts to work after having started (and unmuted) the video manually (using the twitch UI) on the same URL once and then refreshing (testing after in incognito mode doesn’t work again) - might be related to Chrome’s media engagement index (https://developers.google.com/web/updates/2017/09/autoplay-policy-changes).
Firefox somehow does not unmute at all.
The youtube embed API manages to somehow handle these cases.
[edit: just saw you already mentioned the engagement index - would be nice if the twitch API could copy the magic that the youtube api is doing for making it work regardless]