Why do you not have root? This isn't a case of unauthorized use is it? If you are paying for a VPS you should have root. I can't knowingly support anything devious

Side note: I personally would run Jellyfin on a Intel minipc for hardware acceleration.

If you don't have root is it really a VPS?

Anyway, unpack the binaries to ~/local/usr/bin and add that to your PATH.

Jellfin can be configured to use specific installed versions of ffmpeg.

If you do need the jellyfin-ffmpeg (which is needed in specific installs) then you can download releases from github or build it yourself. They do have portable releases.

You do not necessarily need root access to use software on Linux unless you're trying to install it to be available to all users. Users can often install their own software either binaries or compile themselves (unless the system has been locked down). They could sit within your /home/username/bin directory instead of the system level folders like /usr/bin normally used for non-root executable. Your home bin folder is only accessible and so runable by you, and is viable if you do not have access or permission to install into /usr/bin.

You can configure jellyfin to run within your home bin folder or run other software within that folder.

You can get the jellyfin ffmpeg source and releases including portables from their git: https://github.com/jellyfin/jellyfin-ffmpeg

I run it in podman in user context, root is not required

Why not use a docker image?

I run it in Podman rootless