Add real-time booking collaboration via WebSocket

- Backend: /ws relay endpoint (@fastify/websocket)
- Frontend: useHotelSocket hook with lock/unlock/booking events
- Calendar: lock overlay with diagonal stripes shows other manager editing

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/package.json

@@ -14,6 +14,7 @@
     "@fastify/helmet": "^11.1.1",
     "@fastify/jwt": "^8.0.1",
     "@fastify/rate-limit": "^9.1.0",
+    "@fastify/websocket": "^11.2.0",
     "bcryptjs": "^2.4.3",
     "fastify": "^4.28.1",
     "ioredis": "^5.3.2",