I'd have thought it was less hassle to use the jellyfin OCI container in either docker or podman. podman will even generate the systemd service file for you
Docker/podman are not virtualisation, they are containerisation. The system groups all the processes into a namespace and executes them on the same host/kernel as the base system. There is no overhead of virtualisation as its not creating virtual hardware or running a whole OS. Its more like the flatpak you're already running than a vm
Docker and Flatpack are both containerization technologies and work in similar ways under the hood. Docker is more geared towards running headless services that other systems access while flatpack is more geared towards desktop gui applications that are interacted with from the same system they run on.