With tvOS15 beta, my HomePod mini's stopped working as default audio output. They will connect but no sound. However, if I set default to TV output and select my HomePod mini stereo pair via the home button, they work fine.

Have you tried to create a new backup versus using a previous backup? Often when I run into a TM backup issue its usually after an OS upgrade. I've usually solved this by creating a new backup. From that point, updates thereafter work without a problem

You can't revert to an earlier OS. Only thing to do is turn off beta updates and allow the official release version to catch up to your beta.

I previously had my HomePod mini's set as the default audio on my ATV-4K. Following updating to the latest TV beta, the HomePods showed as connected as the default audio but no audio came through. ATV displayed a Airplay message on screen...."Try again(to connect) or change default audio. I reset everything ...still no luck. Then (by accident) I set default audio to TV Speakers and selected my HomePod minis by pressing and holding the Home Screen button. I selected Airplay and HomePod mini's and audio worked!!! So my suspicion is the latest beta has some issue with airplay when selected as default audio but not temporary audio.

I got this message also. Resolved by: 1)removing the previous beta profile, 2)restarting the HomePod, then 3)installing the IOS 15 Beta profile. My HomePods and minis updated just fine to IOS 15 afterwards

...also, the same results occur when trying to use the Remote App on my iPhone to control the Spectrum app. Swiping used to work with the Remote app on my iPhone using the Spectrum app....but not since beta 3