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>

backend/migrations/071_chat_notifications.sql

@@ -0,0 +1,15 @@
+-- Make sender_id nullable to support system messages
+ALTER TABLE chat_messages ALTER COLUMN sender_id DROP NOT NULL;
+
+-- Add system message fields
+ALTER TABLE chat_messages ADD COLUMN IF NOT EXISTS is_system   BOOLEAN NOT NULL DEFAULT false;
+ALTER TABLE chat_messages ADD COLUMN IF NOT EXISTS system_name TEXT;
+
+-- Expand room type to include notifications
+ALTER TABLE chat_rooms DROP CONSTRAINT IF EXISTS chat_rooms_type_check;
+ALTER TABLE chat_rooms ADD CONSTRAINT chat_rooms_type_check
+  CHECK (type IN ('general', 'direct', 'notifications'));
+
+-- One notifications room per hotel
+CREATE UNIQUE INDEX IF NOT EXISTS uniq_chat_rooms_notifications_hotel
+  ON chat_rooms(hotel_id) WHERE type = 'notifications';