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/app.ts

@@ -7,6 +7,7 @@ import rateLimit from '@fastify/rate-limit'
 import { config } from './config'
 import './types' // side-effect: augments fastify types
 
+import wsRoutes          from './routes/ws'
 import authRoutes        from './routes/auth'
 import hotelsRoutes      from './routes/hotels'
 import roomsRoutes       from './routes/rooms'
@@ -62,6 +63,7 @@ export async function buildApp() {
   fastify.get('/health', async () => ({ status: 'ok', ts: new Date().toISOString() }))
 
   // ── Routes ─────────────────────────────────────────────────────────────────
+  await fastify.register(wsRoutes)
   await fastify.register(authRoutes)
   await fastify.register(hotelsRoutes)
   await fastify.register(roomsRoutes)