See all the 1-star ratings in Galaxy Store for Samsung Music. They are are valid - app was broken on my Gear S3 with Note 8 to play music. App wouldn't show or control what was playing on phone, but it worked great months ago. Samsung wasn’t fixing, so all the 1 stars. But I think I stumbled on a solution. Here are two solutions that can work - check out #2, backup & restore:
1. Phone Upgrade: Just upgraded from Note 8 to S22 Ultra. Now the app works well on Gear S3. After changing watch to new phone, I found all watch apps needed updates, which I did. (I also found old watch faces no longer supported or available, dang - whole other problem.) But reset is the key to proposed fix below.
2. Watch Reset (only for adventurous): On watch: Settings> Connect to new phone>(scroll to bottom) Back up data (complete action on phone). Ensure health data is synced. Then, follow through on connecting to “new phone” but actually same phone. Restore backed up data. Update all apps on watch EXCEPT Samsung Music. Maybe the reset version will work better?