Phase 4: Web Push notifications (pywebpush + VAPID)

Backend: PushSubscription model/migration, VAPID config + `cli.py
generate-vapid-keys`, push_service.send_push_to_user (upsert-by-endpoint
subscribe/unsubscribe, auto-cleanup of expired 404/410 subscriptions),
/api/push/* router, and ConnectionManager now tracks connected user IDs
per room so chat.py can push only to offline members after broadcasting
to online ones.

Two test-infra bugs found and fixed along the way: send_push_to_user
takes the caller's AsyncSession and is awaited inline rather than fired
via asyncio.create_task with its own session (background tasks were
outliving the test event loop); and the ws_client fixture now uses
NullPool to eliminate a connection-pool checkout race that was failing
WS tests intermittently.

Frontend: service worker rebuilt with vite-plugin-pwa's injectManifest
strategy (custom src/sw.ts) so it can add push/notificationclick
handlers alongside the existing precaching and StaleWhileRevalidate
routes ported over from generateSW. New subscribe/unsubscribe flow
(lib/push.ts, api/push.ts) with a toggle in the account menu.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/main.py

@@ -2,7 +2,7 @@ from fastapi import FastAPI
 from starlette.middleware.sessions import SessionMiddleware
 
 from app.config import settings
-from app.routers import auth, health, invites, rooms
+from app.routers import auth, health, invites, push, rooms
 from app.ws.chat import router as ws_router
 from app.ws.connection_manager import ConnectionManager
 
@@ -24,6 +24,7 @@ def create_app() -> FastAPI:
     app.include_router(auth.router)
     app.include_router(rooms.router)
     app.include_router(invites.router)
+    app.include_router(push.router)
     app.include_router(ws_router)
 
     return app