feat: housekeeping automation — auto-task on checkout + room status on done

Backend:
- Migration 023: housekeeping_settings table (checkout_auto, checkout_priority, inspection_after_clean)
- New route: GET/PATCH /api/hotels/:slug/housekeeping-settings
- bookings.ts: on checked_out → auto-create turnover task + mark room dirty + broadcast WS
- housekeeping.ts: on task done → update room status (inspect|clean per setting) + broadcast WS
- ws.ts: export broadcast() for use in other routes

Frontend:
- HousekeepingPage: load/save settings to API, live Loader on save button
- useHotelSocket: add housekeeping WS message types
- HousekeepingPage: subscribe to WS — new tasks appear instantly without refresh
- BookingModal: show total section when room + nights selected (not just when total > 0)

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

backend/src/routes/housekeeping.ts

@@ -1,5 +1,7 @@
 import { FastifyPluginAsync } from 'fastify'
 import { db } from '../db'
+import { getHkSettings } from './housekeeping-settings'
+import { broadcast } from './ws'
 
 type SlugParam   = { Params: { slug: string } }
 type SlugIdParam = { Params: { slug: string; id: string } }
@@ -118,7 +120,21 @@ const housekeeping: FastifyPluginAsync = async (fastify) => {
         values,
       )
       if (!rows[0]) return reply.code(404).send({ error: 'Task not found' })
-      return rows[0]
+      const task = rows[0]
+
+      // When task is marked done → update room housekeeping status
+      if (request.body.status === 'done' && task.room_id) {
+        const settings = await getHkSettings(hotelId).catch(() => null)
+        const newRoomStatus = settings?.inspection_after_clean ? 'inspect' : 'clean'
+        await db.query(
+          `UPDATE rooms SET housekeeping_status = $1 WHERE id = $2`,
+          [newRoomStatus, task.room_id],
+        )
+        broadcast(slug, { type: 'housekeeping_done', taskId: task.id, roomId: task.room_id, roomStatus: newRoomStatus })
+      }
+
+      broadcast(slug, { type: 'housekeeping_updated', task })
+      return task
     },
   )