I've encountered a similar issue. My HomePod no longer plays any of my playlists, nor does it play specific song requests — I get the "I can't find that music in your library" error (I am only an iTunes Match subscriber, not an Apple Music subscriber). AirPlay functionality is still working.
I did extensive research on Apple's support forums — I tried resetting the HomePod, removing the HomePod from my HomeKit app and setting it up again, turning my router, iPhone, iPad and Apple TVs off and turning them back on, signing out of iCloud, etc. None of the suggested solutions worked.
I contacted AppleCare support last night, and they suggested turning off Recognize My Voice on HomeKit on my iPhone, which also did not work.
I suspect that the issue may stem from the 13.2.1 HomePod update, since this is a fairly new occurrence for me. Apple said their engineers are aware of the issue and are working on a fix, but they did not have a timeline, nor did they disclose how many units were potentially affected.
I bought a second HomePod last week and have been reluctant to set it up. If this issue persists, I may return the item, since my faith in the device is a bit shaken right now.
I know this doesn't help anyone who's experiencing the issue, but know that you've got company.