fix(studio): hide chat panel before login and center auth loading spinner

Agent-Logs-Url: https://github.com/objectstack-ai/framework/sessions/5fb6f6a0-3113-43a8-be7f-fe05b9313bad

Co-authored-by: xuyushun441-sys <255036401+xuyushun441-sys@users.noreply.github.com>

Author: Copilot

apps/studio/src/routes/__root.tsx

@@ -82,7 +82,7 @@ function RequireAuth({ children }: { children: React.ReactNode }) {
 
   if (loading && !user) {
     return (
-      <div className="flex min-h-screen items-center justify-center bg-background">
+      <div className="flex min-h-screen w-full flex-1 items-center justify-center bg-background">
         <div className="h-8 w-8 animate-spin rounded-full border-4 border-muted border-t-primary" />
       </div>
     );
@@ -107,6 +107,12 @@ function RequireAuth({ children }: { children: React.ReactNode }) {
   return <>{children}</>;
 }
 
+function AuthedAiChatPanel() {
+  const { user } = useSession();
+  if (!user) return null;
+  return <AiChatPanel />;
+}
+
 function RootComponent() {
   const client = useObjectStackClient();
 
@@ -132,7 +138,7 @@ function RootComponent() {
                   <Outlet />
                 </RequireAuth>
                 <Toaster />
-                <AiChatPanel />
+                <AuthedAiChatPanel />
               </ProductionGuardProvider>
             </SidebarProvider>
           </ErrorBoundary>