Alice will not be logged in into the server.

Tailscale allows Alice to merely connect to the IP/port, but whatever service is listening on that port still behaves as usual. So if you have an HTTP service that requires Basic auth, that's still required. If it's a MySQL server, still need an account there to login. If it's SSH, you still need a key/password - or whatever your SSH authentication mode is.

Think of Tailscale like a "jet bridge" securely connecting a bunch of buildings - you can use it to walk up to the front door safely (and Tailscale ACL controls traffic inside the tunnels), but to get inside you still need a key for that door (or whatever your auth method is).