I feel you bro: switching gaming headset to regular HDMI output is a pain in the ass every time.
More details: I have nari ultimate headset, with 2 channels, one for chat, one for games. I only use it TI game with friends, rest of the time I use HDMI regular output. I use discord on Firefox.
Here it comes: im watching YouTube with the HDMI output. Then, gaming time, log on discord (web) in Firefox, turn on headset. Wrong ! My friends can hear me, but I can't. No matter what I click in this applet that you screenshoted, Firefox always defaults to the HDMI output. The workaround: I need to turn on headset first, then open firefox. Then it works.
So it's like firefox doesn't know that the headset is on. Like it cannot detect it, or doesn't process the notification or something. Maybe wrong dbus message ?