My setup is lidarr+airsonic. This setup fulfills all the requirements you listed. The webplayer is really good and you can use free apps to stream your library on mobile devices. Highly recommend “substreamer” for iOS and android. To access my library at home, I use Twingate (Zero Trrust Access VPN that uses the QUIC protocol and it’s lightning fast). Also, the mobile app allows for offline playback and has cool playlist builder features.
I use lidarr to manage my existing library and use airsonic to listen to it. For me it works great and I can import tracks from my Spotify playlist. But yeah, it’s more of a nice to have, for me personally. I use it mainly to keep things tidy.