iPhone music library not updating?

On her iPhone:

Settings﹥Music﹥Show Apple Music﹥On

Settings﹥Music﹥iCloud Music Library﹥On

Apple Music Family doesn’t have an “our library”. Each iCloud Music Library is individual per user. Each user will have to ‘build’ their own library. You share the subscription: access to the service.

You can listen to all the music in the entire Apple Music catalog, not limited to the library of your s.o.

If you also activate the purchase sharing option, then family group members can also access each other’s iTunes Store purchases, including music bought from the iTunes Store. But that is different/separate from music from the Apple Music subscription.

To share items in your library (that are also in the Apple Music catalog) with other subscribers, including Family Sharing group members, you can create and share one or more playlists.

To share unmatched items with other family members, they will have to add those tracks to their own iCloud Music Library through iTunes on a computer.

Isn't access to each others' libraries the entire point of family sharing?

No.

The point is to share the subscription price. The actual music in the iCloud Photo Library is independent to each Apple ID.

As noted, you can share purchased iTunes music via family sharing, but Apple Music tracks are tied to each Apple ID. You can share playlists.