Jellyfin MPV Shim does what you want. MPV is an open source media player like VLC, with more focus on embedded use cases (e.g. mpv is an option in Findroid, a Jellyfin Android app).
The MPV shim runs in the background and appears in Jellyfin (web or app) as a Cast device.
It’s awesome since mpv has many keyboard shortcuts I’m missing with Jellyfin.