The Gelatinarm client can stream music from a Jellyfin server in the background but it doesn't support the SyncPlay feature.
People talk about the death of social media but with Plex killing Watch Together last year you can barely tell that anybody ever tried.
The easy way to pipe Jellyfin -- or any audio -- into an Xbox-Discord game chat is to use Blackhole to make your audio out an audio input and then pipe that into the Discord chatroom via a 2nd account that DJ's the music. Other users can control the jukebox by signing into the Jellyfin SyncPlay session.
To make command line aliases to swap the audio back and forth between the system and the pipe you can install switchaudio:
SwitchAudioSource -t input -s 'BlackHole 2ch';SwitchAudioSource -t output -s 'BlackHole 2ch'