I hope someone else knows a better way to do this because it would appear it is somewhat possible but not easy.

Subsonic servers, such as navidrome, offer the ability to "SyncPlayQueue" via api to specific players, but in the case of navidrome that does not included the web player or music assistant for home assistant (the later is an assumption as i was unable to find a setting to enable it).

For those who don't care about home assistant they just need to find a player on the devices they want to transition music too and from that supports the feature.

For those who use home assistant and want to listen to music across devices you can transfer queue from within the music assistant player to a device added as a player or the app by picking "this device". That only works if you've been playing music from your phone on a smart speaker, the music queue being played via web isn't visible from the app and vice vera. It might be possible to set a web browser as a player to interact with but i imagine that would be a fragile setup at best.

I haven't tested this, but Jellyfin does this with videos and ebooks so I'd be surprised if it didn't also work this way for music.

Jellyfin is FOSS and entirely self hosted.

It's not FOSS, but Plex does that. I host my music from a server I built at home (you can literally just use your desktop PC) and then I have access to it from anywhere. I like to stream it to the Plexamp app on my phone, which I connect to my car via Bluetooth, then I have my own homemade "radio" on the go. No ads, just my own music that I can shuffle through.

I paid for the Lifetime Plex Pass, which gave me full access to all their features and apps. It's expensive, but it's a one-time payment, vs. their monthly subscription which can add up over time.

I actually got annoyed at Plex for remembering exactly where I was in every song. I'd return to an album I hadn't heard in a while and it would skip right to where I left off in each song instead of playing from the beginning of the song

Sometimes while trying to find a particular song, I'd skip around in a track, then move to the next until I found it. Then when I returned to that album later, every song would start somewhere in the middle. I eventually needed to turn that feature off. It still remembers exactly where I left off the last time I played music, but it doesn't save my place in each individual song anymore. Just the last one I played.

On the app, it keeps a list of all the playlists I've recently played, so I can pick up on my latest playlist or scroll back in the history and start up one I played a while ago. This is great because I like to just shuffle my entire library as a playlist while I'm mowing my lawn, but my wife likes to hear specific genres or bands while we're riding in the car together. So I can just keep alternating back and forth between playlists depending on the situation and it remembers where I left off in each one.