

No, each server is accessed separately. You can swap between servers easily, but there is no central way to browse all of your servers simultaneously. Jellyfin was designed specifically to rebel against Plex’s centralization, so that’s not a feature they’re ever likely to implement. There are ways to sync your watch history between servers, but it’s using third-party plugins.
“Just give the bully your lunch money, and they’ll stop asking for it in the future. It definitely won’t result in them coming back tomorrow to shake you down again.”