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/pnpm-lock.yaml

@@ -20,6 +20,9 @@ importers:
       '@radix-ui/react-slot':
         specifier: ^1.3.0
         version: 1.3.0(@types/react@19.2.17)(react@19.2.7)
+      '@tanstack/react-query':
+        specifier: ^5.101.0
+        version: 5.101.0(react@19.2.7)
       '@tanstack/react-router':
         specifier: ^1.170.16
         version: 1.170.16(react-dom@19.2.7(react@19.2.7))(react@19.2.7)
@@ -916,6 +919,14 @@ packages:
     resolution: {integrity: sha512-79pf/RkhteYZTRgcR4F9kbk84P2N8rugQJswxfIqovlbRiT3yI7eBE+5QorIrZaOKktsgzRlXh1l/du/xpl4iA==}
     engines: {node: '>=20.19'}
 
+  '@tanstack/query-core@5.101.0':
+    resolution: {integrity: sha512-cQetA74EB+seWySv1TTKr828TnP0u39m6LykwDXIo84SNortpDkp30TMEjkqtYCNP9c40uT/iwl6MLiufEt0Ow==}
+
+  '@tanstack/react-query@5.101.0':
+    resolution: {integrity: sha512-rLlJXSpkqfizLWgkR5+eLeIk0MvTx/meEIR7LRjxic+qxiQP8zVjq7BqQkiCMNLQBlLfuOLqqr6KO5GtrDlmSg==}
+    peerDependencies:
+      react: ^18 || ^19
+
   '@tanstack/react-router@1.170.16':
     resolution: {integrity: sha512-w6eq1IJklujs1tESazaK/FxH0+H2l8vm/QPuu1cD3oRW/ubgKneQpd7b64ti/8gUyEimzimJQZDmJr6YHfP5+g==}
     engines: {node: '>=20.19'}
@@ -2903,6 +2914,13 @@ snapshots:
 
   '@tanstack/history@1.162.0': {}
 
+  '@tanstack/query-core@5.101.0': {}
+
+  '@tanstack/react-query@5.101.0(react@19.2.7)':
+    dependencies:
+      '@tanstack/query-core': 5.101.0
+      react: 19.2.7
+
   '@tanstack/react-router@1.170.16(react-dom@19.2.7(react@19.2.7))(react@19.2.7)':
     dependencies:
       '@tanstack/history': 1.162.0