Define "slow". Pages hang before loading? Or it often stops to buffer a stream?

don't know what "slow" means in your case, but jellyfin clients have a buffer setting and increasing it should improve things for them.

I am in basically the same situation as you and my single asian user has no issue with it

Tailscale, headscale, or something along those lines may help optimize the route but as others have said to resolve this is an actual fashion you'd need a cdn which requires significant geo-redundant hardware which comes at a pretty significant cost. That being said I think your friend has a good shot if you implement the former.

You're describing a CDN. You can't afford it.

I'd look more into boosting whatever your uplink is versus trying to distribute to localized users.

Even large streaming services drop their servers close to the users to make the experience good. They just do better at scaling.

You could federated authentication so only one ldap service is maintained. You could also sync media from one device to the other so you don’t need to manually update both.

You unfortunately cannot solve this yourself, this is where 800lb gorillas like akamai outclass self-hosted.

Netflix alone has many thousands of isps participating in Open Connect alone, these providing CDN peering points all over the world and making Netflix only a few hops away for more end users.

You don’t necessarily have to host another Jellyfin instance, I would find a server somewhere in-between the middle of your current Europe server and your Asian homies and setup a reverse proxy there and point it to your current Jellyfin instance.

The only hassle with this is you’re going to need a way to expose Jellyfin to it, a VPN would prevent port forwarding 443, perhaps split tunneling?

Not the most elegant solution but at least this way you can make an attempt at optimizing the connection.

Edit - (if you wanted to go the second Jellyfin instance route): Could also copy your current database to the second server, host a second Jellyfin instance and have something like sshfs or sftp sharing the directory to your media library, reverse proxy it as something like asia-jellyfin.your.domain and keep it separated from your Eu server.

IMHO Jellyfin is processing everything it sent to clients. So I do not think it possible to put it behind SDN( may be it possible if server side transcoding is off) Please define slow. Slow on what part? It should be like 250ms RRT to your server which is not much for web-based apps.

This may be completely untrue but maybe the remote users could get a vpn with a server near yours? Without having the slightest idea that it does I could imagine it could help.