Phase 3 scaffold: chat engine (WebSocket, FCM, pricing, timer, extension, history)

- Backend: WebSocket plugin, chat/pricing/timer/extension/closure/notification services
- Client app: ChatBloc, pricing dialog, chat screen with message status, extension/goodbye flow, history
- Mitra app: MitraChatBloc, ExtensionBloc, chat screen, extension accept/reject, history
- Control center: free trial, extension timeout, early end config toggles
- DB migration: chat_messages, session_closures, session_extensions, customer_transactions tables

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/package.json

@@ -13,6 +13,7 @@
   "dependencies": {
     "@fastify/cors": "^9.0.1",
     "@fastify/sensible": "^5.6.0",
+    "@fastify/websocket": "^11.2.0",
     "dotenv": "^16.4.5",
     "fastify": "^4.28.1",
     "firebase-admin": "^12.2.0",