You have to go to the "Configuration"-tab in the window (upper center/right of the picture), in there you can configure which HDMI/DisplayPort-port your card uses for output. It will of course differ depending on which port you use for the HMD. Best way to figure out: Start beatsaber and get to the main-menu (there will be music playing there), then try out the different ports for your card under the Configuration-tab until you hear something. It is important that you pick the port under configuration, then go back to the "Output devices"-tab (your picture) and re-select your output (it resets to some other output every time you change the port under Configuration).

When you figure out, memorize the port, you'll have to set it each time you start SteamVR because the port disappears and become invisible to pulseaudio every time you turn off SteamVR (and resets to some other available source/output.

There's probably some way to script it, at least I remember seeing some once, but couldn't get it to work, so I just set it every time.

For some reason Pop OS has a more sane layout in its sound settings, the different active ports actually become selectable under the "Port"-equivalent in your image.

The workaround given by @ZarathustraDK worked for me... But it seems to me that if SteamVR is firing up, it should set the OS playback device to whichever HDMI port the HMD is plugged into. Right?

In other words, I'm not sure that this issue should be closed just yet.

Commenting because I had this issue too and this thread appeared in DuckDuckGo: Make sure udev rules are set exactly as described in the README! That got things working for me (as in, I was able to change the port my card was using to the Index).