ITunes Match Does Not Work on New HomePod Minis

I have searched and searched for a 2023 solution to this issue…

I have a big iTunes Match library going back to the old iPod days. The only way I can get Siri to play anything from it is by using AirPlay. Even asking her to play something with the iPhone facedown and nowhere nearby results in AirPlay activating and the iPhone getting hot because it’s using battery.

What on Earth? How can I access iTunes Match and NOT use AirPlay? The HomePod Minis have been up and running for nearly a week, and have updated software. Sync is activated in my music settings. There has been plenty of time for the sync to have happened.

I have always bragged to my Android friends about how the Apple ecosystem just WORKS. No muss, no fuss. I guess not with these! The HomePod marketing says it works with iTunes Match. This is clearly a lie.

I am so angry and frustrated. If I wanted to AirPlay and use up iPhone battery, I could have just saved myself a boatload of money and kept my old Google Minis and listened via Bluetooth. I am ready to return these. Can anyone help? Are there instructions somewhere that I am missing?