How do I set up my generation 3 appletv with my HomePod mini

Hmm, I don’t have that Apple TV to check compatibility on if a Mini can be used and it’s not mentioned in the Specs. I believe you look in Settings> Audio & Video.> Audio Output and select your HomePod or it might be in AirPlay settings

I've got an Apple TV 3, but I cannot find its remote. See AirPlay system requirements - Apple Support. As far as I can tell Apple TV 3 supports AirPlay 1, HomePods work with AirPlay 2. So no dice.

tt2

I remembered that I can use my iPhone as a remote for my old Apple TV 3. What do you know? The HomePods show up as potential AirPlay targets, though Apple TV 3 doesn't see the stereo pairs. Anyway you can AirPlay from Apple TV 3 to HomePod or HomePod mini.

tt2