I just gave it a shot, by running:
$ podman run --rm -it -p 8096:8096/tcp jellyfin/jellyfin
And I get the "Welcome to Jellyfin!" page, which lets you set the language/setup a user account. So I think in general if you are just running the OCI image it is not typically expected to see the server list. (I'm sure it's still possible to get to, and presumably you can wind up there if some RPC fails.)
That said, I might've found a clue: if you re-run it, you get another randomized hostname, and then you get the server select page. If I clear cookies and reload, it again skips the server select page. So it seems like if you have the hostname of your jellyfin instance change, say, by starting a new Docker container with a different name, but have it accessible at the same place, that might cause this weirdness.
Other issues may include improperly configured reverse proxies. (If you're using a reverse proxy, you should make sure it's configured right for Jellyfin's websockets and CORS usage and potentially some other stuff.)