feat: PWA push notifications — service worker, VAPID, subscription management

- Add web-push VAPID backend with push_subscriptions table (migration 078)
- Backend push module with sendPushToUser/sendPushToRoom helpers
- Push routes: GET vapid-key, POST subscribe, DELETE unsubscribe
- Trigger push on new chat messages in direct/group rooms
- PWA manifest, service worker, and icons (72–512px)
- Frontend push lib: SW registration, subscribe/unsubscribe helpers
- Push API in api.ts, SW registered in main.tsx
- usePushSubscription hook for auto-subscribe on permission grant
- PushPermissionRow component in ChatWidget settings view

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

backend/package.json

@@ -17,11 +17,13 @@
     "@fastify/rate-limit": "^9.1.0",
     "@fastify/static": "^7.0.4",
     "@fastify/websocket": "^8.3.1",
+    "@types/web-push": "^3.6.4",
     "bcryptjs": "^2.4.3",
     "fastify": "^4.28.1",
     "ioredis": "^5.3.2",
     "nodemailer": "^8.0.2",
-    "pg": "^8.12.0"
+    "pg": "^8.12.0",
+    "web-push": "^3.6.7"
   },
   "devDependencies": {
     "@types/bcryptjs": "^2.4.6",