

Syncthing is not just for LAN use. Even their homepage mentions transmitting data over the internet
I’ve been using it to sync devices over the internet for years. It’s also how people use it to sync from say their desktop to their phones, remote server, etc.
If you watch your network firewall Syncthing does reach out to servers on the internet to help it find other devices so e.g. if you enter the other device’s ID (example ABCDEFG-ABCDEFG-ABCDEFG-ABCDEFG-ABCDEFG-ABCDEFG-ABCDEFG-ABCDEFG) it can reach out over the internet to find that specific ID to pair with. I think Syncthing uses a sort of DHT resolver to find other devices, I know on my firewall I had to whitelist Syncthing’s servers to make it work.
I was going to try to link you some references but their forums seem to have connection issues at the moment, you may want to search around later if you’re interested how Syncthing works over the internet.
Should be able to do that with Jellyfin, no Plex/Plex Pass needed (if you really want to use media software for this).
That said I suspect your current method with creating a torrent to share is much more resilient when dealing with choppy internet connections. With Jellyfin/Plex it’s more of a direct download situation, not sure if either can resume broken downloads.