I can't open my Apple Music library on my Mac

I subscribed to Apple Music via my iPad. All went well. I built a few playlists.

The app on my iPhone automatically kicked in to the subscription and showed the playlists.

But when I opened the app on my Mac desktop, it doesn’t recognize my subscription and wont show my library or playlists.

Am I doing something wrong?

What’s the solution?

[Re-Titled by Moderator]