I made a quick and dirty (emphasis on dirty) app to do that. You upload your own music and m3u playlists and get a link to share with your friends. The master controls what's played and that is synchronised to everyone. We used it to control music for our remote D&D sessions.
https://github.com/bjoern-tantau/share-your-music
The code and interface are really ugly. And I cannot provide support because I'm disabled. But it can serve as a proof of concept.