Admin console: show the signed-in operator's name, not "Administrator"

The user switcher fell back to "Administrator" whenever /admin/api/status
returned no currentUser. Fresh sign-ins already embed the verified Emby
account name in the session cookie, but a session minted before that field
existed (or one that has not been re-issued since) is valid yet anonymous,
so the fallback showed for ever.

handleAdminConsole now treats a valid-but-anonymous admin session as needing
a fresh sign-in for the SPA shell only — a one-time prompt that fills the
name in, since session renewal preserves whatever the cookie already held.
Asset requests are unaffected, so nothing breaks mid-session.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011wS9Qz3Fkxeu9KPt26hhhx

server/internal/api/installer_auth.go

@@ -164,6 +164,17 @@ func (s *Server) validAdminSession(r *http.Request) bool {
 	return ok
 }
 
+// adminSessionNamed reports whether the request's admin session carries the verified Emby
+// account name. Every session minted since the identity was added to the cookie has one;
+// a session predating it is valid but anonymous, which is what makes the console's user
+// switcher fall back to "Administrator" instead of showing who is signed in. The console
+// document handler treats an anonymous session as needing a fresh sign-in so the name is
+// picked up — a one-time prompt, since renewal preserves whatever the cookie already held.
+func (s *Server) adminSessionNamed(r *http.Request) bool {
+	_, username, ok := s.browserSession(r, adminSessionPurpose)
+	return ok && username != ""
+}
+
 // renewAdminSession slides a valid session's expiry forward. The TTL was absolute and
 // nothing extended it, so an operator working the admin console was signed out from under
 // themselves and the page's poll became a permanent "invalid admin