This is why I talked about allowing local traffic.
I’m going to try and keep this newbie friendly (but I’m not the best at it, so let me know if something is not clear).
In an ideal world everything has an IP address that is unique. Some portion of the denotes it’s network, some portion denotes the host. In this way we can define logical (and oftentimes physical) associations. Your home is a classic example of a local area network (LAN).
So what does a vpn do? It makes a tunnel that connects your machine to a remote network, forming a logical connection and “relocating” your device. In the VPN config you should have the option to allow local access. This will set up some fun rules for how network traffic is routed - if it’s going to a LAN address it can, otherwise all traffic is routed over the VPN.
Ok.
I’m going to warn you right now. Unless you want to do some reading on how traffic is routed, how Linux handles VPN connections and (probably) containers, do not run the clients that download content on your media server.
If you want to use jellyfin to distribute media in a lan you do not need to do anything other then just start the jellyfin server on the pi and add content.