Music Rover, an app for finding your favorite songs in Apple Music, now also allows you to browse and play your music library in v1.1.0! (iOS 16 and above)
You can switch between Home/Library/Search from the icon in the upper right corner.
The recommended use is to start a station from a favorite song in your library. When you start a station, the related song will automatically play. Try long pressing a song to add it to the station queue.
Music Rover is a music player app with an emphasis on clean design, and I hope you enjoy its simple UI not only for playing Apple Music content, but also for playing your music library.