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/package.json

@@ -19,6 +19,7 @@
     "@radix-ui/react-dropdown-menu": "^2.1.18",
     "@radix-ui/react-label": "^2.1.10",
     "@radix-ui/react-slot": "^1.3.0",
+    "@tanstack/react-query": "^5.101.0",
     "@tanstack/react-router": "^1.170.16",
     "class-variance-authority": "^0.7.1",
     "clsx": "^2.1.1",