I dont know about the HomePod Mini because I don't have one but my AirPlay 1 speakers stopped working with tvOS 15.0. AirPlay 2 speakers seems to work but not AirPlay 1. If I manage to get an AirPlay 1 speaker to work temporarily the sound is out of sync. The problem persist with the latest beta.

The default speaker selection in tvOS 15.0 is a disaster for me using a projector. I just selected my AirPlay speaker in previous version of tvOS and it worked beautifully and the selection persisted over time. Just the way I wanted it. With tvOS 15.0 I can no longer select my AirPlay speaker as the default speaker. The only option is my projectors small and lousy built in speakers. My AirPlay speakers can only be selected as temporary speakers and this selection doesn't persist. This is pretty annoying since I now have to manually first have to deselect the projectors built in speakers and then select my AirPlay speaker as a temporary speaker. This setup doesn't persist so I have to do it each time I want to watch TV on the projector. Dear developers, please consider other use cases than the Apple TV hooked up to a TV set or a HDMI enabled amplifier. Think a projector in the ceiling where the HDMI cable has to go, with built in speakers that has to be bypassed and sound being routed to a sound system another 20 meters away. That is my situation and my Apple TV 4k has worked perfectly in this setup for years until tvOS 15.0 totally broke it. These problems together with sound being out of sync to AirPlay 1 speakers persist with the latest beta.