Have you tried Piper?

They probably run it more than once a week :)

I was using Plexamp for a while but now I’ve mostly converted my library to OPUS so I can fit it all on my phone. I have a script to automatically copy the directory structure/artwork and convert from my main FLAC library, and keep it in sync with my phone using syncthing. I use Musicolet for playback. If your library is bigger or you don’t have much free space then this is of course not an option, but it works for me.

This is not to counter your point (I agree they should probably offer a client to sync files on Linux), but rclone recently added (beta) support for proton drive, so you might want to check that out if you’re still using it.

Not sure about Jellyfin, but Plex would transcode to a format supported by the client yes.

I’m not sure about pulseaudio but snapcast is time synced.