airfoil will do it, but completely unneccsary. also involves adding hardware (a laptop) and purchasing software you don't have to.
when you say "my Apple Music" you're just referring to the streaming service? and not songs you've added to your Mac?
one way
on the HomePod mini with music playing, ask siri to "play this everywhere"
as long as your airplay speakers are
added to the home app, that should work.
if you've also assigned rooms in the home app, you can ask siri to "play this in the kitchen" and the HomePod will send audio to the kitchen speaker. or with zones, "play this downstairs"
another way
on you phone go to the airplay settings in the control center....
- airplay icon in the music tile
- control other speakers (at bottom)
- select one of your HomePods.
now the homepod will be the current player on your phone, hit the airplay icon again, and you can select which speakers you want to send audio to and control the volume.
(sometimes your phone will switch to the hompod automatically. If what the HomePod is playing shows up on your homescreen, you can just hit the airplay icon)
another way
Start something playing on your phone
hit the airplay icon
select the speakers you want to use. (your phone will be deselected, you can do phone or airplay, but not both)