I have the exact same issue. I have tried unpairing, deleting all music, resyncing, restarting my watch and iPhone, turning Bluetooth on and off, unpairing my AirPods, etc. It will work without issues for a few days and then suddenly, the music on my Apple watch just stops playing. I can't make it start again by doing anything - all the troubleshooting tips don't work (and I've searched for weeks). Then I'll try again later and sometimes it works and sometimes it doesn't. The issue isn't consistent.
It's not my AirPods, because they work with phone calls and my iPhone. All Apple music and radio works with my iPhone, but it's very unreliable with the watch. It's especially frustrating when I leave for a walk without my iPhone and it won't work.
I have an iPhone 8 and my watch is a series 3 with an active cellular plan. All my software is always up-to-date. To me, it seems like it's a bug either with Apple Music, or with the watch OS. Either way, this needs to be fixed.