I installed Bazzite today on my home theatre PC for gaming. It has an AMD GPU. I downloaded the home theatre PC edition with a KDE desktop.
There was no sound coming out of the TV via HDMI in Gaming Mode. I switched to Desktop mode and there was still no audio coming out. In the settings app, an audio device for HDMI output was already selected and set to 100%, but no sound was being outputted. Everything looked fine in alsamixer, nothing was muted.
What solved it for me was connecting a Bluetooth speaker and then disconnecting the Bluetooth speaker. For whatever reason, Bazzite out-of-the-box would not play any audio over HDMI, but connecting a Bluetooth speaker and then disconnecting the Bluetooth speaker solved the issue. I only needed to do this once - the issue has not come back even after restarting the computer.
I hope this helps someone else out there who wants to try gaming on Bazzite and who runs into the same issue.