Sadly, I agree that folks are well-advised to verify every single hope and expectation of modern Apple products before buying.
In this case, I chaff at the assertion that "it was made very clear" that this no-brainer feature expectation (that a HomePod mini by Apple can be selected as default sound output using the latest Apple TV 4K when an older HomePod model can) is not supported. I don’t care about the home theater feature even if that effort spawned the default output feature. Why should a buyer need to study a support article about a logically-unrelated feature to learn that Apple TV doesn’t support HomePod minis any better than generic airplay speakers? For that matter, I should be able select 3rd party airplay speakers as default output (but I’ll not hold my breath for that).
Apple should avoid making marketing decisions regarding product functionality that are too awkward to explain in compelling sales copy. I once viewed Apple’s brand with the certainty that Apple products worked insanely great with Apple products.
Sorry (stepping down from soapbox). In this case, I hope and sort of expect that a future version of tvOS will offer better HomePod mini support now that the original HomePod is being discontinued.