How to play music on HomePod mini that I bought on iPhone Music (not the subscription)

Hi all,

My HomePod mini just arrived in the mail today, and I have not been able to get it to play any music from my purchased library. I have AirPlayed music from my phone to the HomePod, but I want an option to play my music hands free.

I do not have an Apple Music subscription, nor do I want one. I bought my most played albums on iTunes/Apple Music app on my iPhone and I am able to play these songs on the Music app of my iPhone, iPad, and computer. However; when I ask Siri on the HomePod to play one of my purchased songs/albums, she either says it's not available or plays the wrong song.

For example, I asked Siri to play Underdog by Alicia Keys, and Siri said she would play Underdog, but instead played a song I've never heard of before from a different artist, with nothing to do with Underdog. Then, I asked Siri to play the album Six: The Musical, and Siri played Underdog. When I ask Siri to play some of my songs or any of my Apple Music playlists, she says she cannot find it. Siri consistently is getting it wrong no matter which song/album/playlist I request.

Has anyone gotten music they bought on iTunes/Apple Music on iPhone to work with the HomePod? Are there any settings I should check/change on my phone or HomePod? Are there any tricks that have worked for people to get the HomePod to recognize my iTunes/Music library?

Are there any other workarounds for playing music hands free that people have found? I've been playing around with asking Siri on my phone to AirPlay music to the HomePod, which has been working, but when my family member asks on their iPhone (with a different Apple ID, but listed as a "Resident" under my Home app), their phone's Siri says they cannot find that speaker. Thus, this workaround for hands free music currently only works if my phone is in the room.

Any and all advice on these topics would be very appreciated. Thank you!