feat: chat — search, notifications room, settings

- Migration 071: nullable sender_id, is_system flag, notifications room type
- Backend: notifications room auto-created per hotel, search messages endpoint,
  notify endpoint (manager/admin posts system messages), read-only enforcement
- API: ChatSearchResult type, chat.search(), chat.notify(), updated ChatMessage type
- Frontend ChatWidget: search view (people + messages tabs), settings panel
  (notifications visibility toggle, sound toggle), notifications room (bell icon,
  read-only banner, amber styling for system messages), new-chat button

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

src/lib/api.ts

@@ -340,7 +340,11 @@ export const api = {
     markRead: (slug: string, roomId: string) =>
       req<{ ok: boolean }>('PATCH', `/api/hotels/${slug}/chat/rooms/${roomId}/read`),
     openDirect: (slug: string, otherUserId: string) =>
-      req<{ room_id: string }>('POST', `/api/hotels/${slug}/chat/direct/${otherUserId}`),
+      req<{ roomId: string }>('POST', `/api/hotels/${slug}/chat/direct/${otherUserId}`),
+    search: (slug: string, q: string) =>
+      req<ChatSearchResult[]>('GET', `/api/hotels/${slug}/chat/search?q=${encodeURIComponent(q)}`),
+    notify: (slug: string, text: string, systemName?: string) =>
+      req<ChatMessage>('POST', `/api/hotels/${slug}/chat/notify`, { text, system_name: systemName }),
   },
 
   // ── Workstations ──────────────────────────────────────────────────────────
@@ -1302,7 +1306,7 @@ export interface LoyaltyTransaction {
 
 export interface ChatRoom {
   id: string
-  type: 'general' | 'direct'
+  type: 'general' | 'direct' | 'notifications'
   name: string | null
   unreadCount: number
   lastMessage: string | null
@@ -1315,11 +1319,24 @@ export interface ChatRoom {
 export interface ChatMessage {
   id: string
   roomId: string
-  senderId: string
+  senderId: string | null
   senderName: string
   senderRole: string
   text: string
   createdAt: string
+  isSystem: boolean
+  systemName: string | null
+}
+
+export interface ChatSearchResult {
+  id: string
+  roomId: string
+  text: string
+  createdAt: string
+  senderName: string
+  roomType: 'general' | 'direct' | 'notifications'
+  roomName: string | null
+  otherUserName: string | null
 }
 
 export interface WorkstationDevice {