Apple Music Family Sharing not working on Child's Apple Watch
Solution found! Go to music.apple.com and sign in with the Child's Apple ID. Browse and add music to their library that way. It will synch to their watch so they can play it. Spent nearly 2 hours with customer service and that is what finally worked.
The Watch app works differently for Family watches and not all features are available, including managing music. Apple IDs are correct, software up to date, family sharing on...but no music would appear until we added it to our child's profile through music.apple.com. Hope this helps someone else.