Unable to get music on wife’s phone while using Music family plan

Make sure she is also invited to join the Family Sharing Plan. And that she has accepted the invitation on her new iPhone. See the "Invite people to join your family" section in:

Set up Family Sharing - Apple Support

Hi, are you also using separate Apple IDs that are linked together as a “family” via Apple’s Family Sharing or do you share the same Apple ID across devices. If you have separate IDs and are using Family Sharing, have you tried going to Settings, clicking the logged in Apple ID at the top of the page and then clicking on Family Sharing to verify that both a) her ID appears in the list of Family Members , and b) Apple Music is turned On in the list of Shared Features. I know you mentioned that Music is turned on in “iTunes settings” but the Music setting on the “iTunes and App Store” settings page corresponds to Automatic Downloads. It’s a little confusing now that the Music app has taken over for iTunes, so I’m not quite sure if you actually mean that you checked the “Music” settings or the “iTunes and App Store” settings. Either way, the settings I’m referring to are under the Settings > [Logged in user’s Apple ID] > Family Sharing.