I bought two HomePod Minis from Apple; they were delivered last week.

It’s not eligible

“when you buy a new iPhone, iPad, iPod touch, Apple TV, or Mac, it includes one year of Apple TV+ for free.”

https://offers.appletvapp.apple/

I don't know what free trial offers are in force at the moment, but I'm not aware of one associated with HomePod mini. Can you point to a web page for this promotion?

tt2

You can get a free trial of Apple Music. I’m not sure how long it’s still for though. Was 3 months.