I think you're on the right track with Wireguard.

I'm also running Jellyfin, but mostly Navidrome for music. I've been pretty satisfied with the latter.

Consuming music outside the house has been a significant issue. I mostly tried to go the offline route: download some music to play while you're out of the house ... and on Android the experience has been overall very poor. My least worst experience was with Substreamer as a client, but still not anywhere near good.

Where I'm at today is with always-on VPN through Wireguard and the experience is significantly better than any other solution I've tried before.

It's been years I haven't played with mpd, so I can't comment on that.