feat(unit-4): Dashboard — availability widget with TanStack Query

- Add @tanstack/react-query 5.101.0; wrap app with QueryClientProvider
- Add AvailabilityStatus type and AvailabilityResponse to api/types.ts
- Implement useAvailabilityStatus (staleTime 30s, stale-on-error preserved)
- Add AvailabilityStatusBadge with green/amber/red states and stale indicator
- Replace DashboardPage placeholder card with live availability widget
- Add MSW availability handler; update test/utils with QueryClientProvider
- 55/55 tests pass (FR-05)

Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>

frontend/src/main.tsx

@@ -1,6 +1,7 @@
 import { StrictMode } from 'react';
 import { createRoot } from 'react-dom/client';
 import { RouterProvider } from '@tanstack/react-router';
+import { QueryClient, QueryClientProvider } from '@tanstack/react-query';
 import './index.css';
 import './i18n/config';
 import { AuthProvider } from '@/contexts/AuthProvider';
@@ -8,6 +9,12 @@ import { useAuth } from '@/contexts/auth-context';
 import { Toaster } from '@/components/ui/sonner';
 import { router } from '@/router';
 
+const queryClient = new QueryClient({
+    defaultOptions: {
+        queries: { retry: 1, refetchOnWindowFocus: true },
+    },
+});
+
 function BootstrapSplash() {
     return (
         <div className="flex min-h-svh items-center justify-center text-muted-foreground">
@@ -43,10 +50,12 @@ void enableMocking().then(() => {
     }
     createRoot(rootElement).render(
         <StrictMode>
-            <AuthProvider>
-                <InnerApp />
-                <Toaster />
-            </AuthProvider>
+            <QueryClientProvider client={queryClient}>
+                <AuthProvider>
+                    <InnerApp />
+                    <Toaster />
+                </AuthProvider>
+            </QueryClientProvider>
         </StrictMode>,
     );
 });