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/src/routes/ws.ts

@@ -0,0 +1,40 @@
+import { FastifyPluginAsync } from 'fastify'
+import fastifyWebsocket from '@fastify/websocket'
+import type { WebSocket } from 'ws'
+
+// hotel slug → set of connected clients
+const hotelRooms = new Map<string, Set<WebSocket>>()
+
+const ws: FastifyPluginAsync = async (fastify) => {
+  await fastify.register(fastifyWebsocket)
+
+  fastify.get<{ Querystring: { hotel?: string; token?: string } }>(
+    '/ws',
+    { websocket: true },
+    (socket, request) => {
+      const hotel = request.query.hotel ?? ''
+      if (!hotel) { socket.close(4001, 'hotel required'); return }
+
+      if (!hotelRooms.has(hotel)) hotelRooms.set(hotel, new Set())
+      hotelRooms.get(hotel)!.add(socket)
+
+      socket.on('message', (raw) => {
+        const data = raw.toString()
+        const peers = hotelRooms.get(hotel)
+        if (!peers) return
+        peers.forEach(client => {
+          if (client !== socket && client.readyState === 1) {
+            client.send(data)
+          }
+        })
+      })
+
+      socket.on('close', () => {
+        hotelRooms.get(hotel)?.delete(socket)
+        if (hotelRooms.get(hotel)?.size === 0) hotelRooms.delete(hotel)
+      })
+    },
+  )
+}
+
+export default ws