Apple Music with Family Sharing activated, but my wife's iPhone 12 SE does not see my library or play lists. How do I make this happen?

If it is music that you purchased from the iTunes Store, then make sure purchase sharing is turned on:L

How to share purchases with your family - Apple Support

If it is music that you lease with an Apple Music Family subscription, then everyone in the family gets their own music library. There is no way to share those libraries. However, you can still share playlists (which are just the names if the songs):

See what friends are listening to in Apple Music on your iPhone, iPad, iPod touch, or Android device - Apple Support