From José Adorno at 9to5Mac:

HomePod and even the new HomePod mini don’t count songs when you ask Siri to play something on your smart speaker. This affects your Apple Music Replay statistics and integration with third-party Apple Music applications.

Play counts with Apple Music have always been wonky. I don’t see this particular issue, but I don’t doubt he’s seeing it. One of the main reasons I use Apple Music over Spotify is the underlying power of play counts and metadata, but relying on it being 100% accurate is a fool’s errand. It’s been abut 5 years since Apple Music launched and I still feel like the fundamentals aren’t quite where they need to be.