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