HomePod Apple Music play counts not updating

When I play AppleMusic songs on my HomePod, they never are listed as recently played.

When I play songs on an AppleTV, an iPhone in my car connected via USB, or macOS, the play counts of a song are updated in the Music app. (Sometimes that takes a day or two to be synced up.) The Recently Played playlist is updated.

I'd like that to happen when I play on my HomePod, too. My AppleID is the main user on my HomePods. When I'm playing a song on music iPhone, and use AirPlay to move it to the HomePod that works fine--except the play counts of the songs that are then played are never updated.

I'm sure there's a setting or technique that I'm missing that could help resolve this. I like being about look back and see what songs I played when.