What version of Apple TV is required for a HomePod mini stereo pair to work?
Unfortunately, Home Theatre Audio does not currently work with HomePod mini (just HomePod). It also seems to require Apple TV 4K. The benefit of this feature is that you can set your Apple TV audio output to permanently use the HomePod pair.
But you should be able to (manually) Airplay to a pair of HomePod Mini’s with an Apple TV that supports tvOS 14 (an assumption, based on its support of being an audio hub): this would mean Apple TV HD or Apple TV 4K.
If you’re buying a new Apple TV and you’re interested in using your HomePod Mini’s as your permanent tv speakers, I would suggest getting the Apple TV 4K with the assumption that Apple will eventually add Home Theatre Audio support for the HomePod Mini’s.