... Make sure that you're using the same Apple ID for Family Sharing and Media & Purchases...
They don't say how to migrate to that idea of course! Obviously it was possible to use a different Apple ID for Family Sharing and Media (Apple Music worked before). I don't know if the changes made to my device impacted any other family members (wish I'd checked!), but it appears for a Family Organizer device to see Apple Music they have to use the same Apple ID used at time of purchase.
Somewhat surprisingly Apple let me revert back to Sam/Linda on my iPhone. (I think there was some time limit/change limit on Apple ID media changes.) After a period of sync I had my old playlist and Apple Music access.
My guess is that to make the change to Sam/Sam and keep Apple Music I'll have to end my current subscription (tied to Linda) then change the Media Apple ID then resubscribe for the family. (In practice I'll end all subscriptions for Linda before the change.)