perf: Redis pub/sub, PgBouncer, optimistic UI for high concurrency

- Add Redis 7 for pub/sub (lobby + chat real-time), rate limiting, caching
- Replace SSE DB polling with Redis pub/sub (lobby: instant approval, chat: instant delivery)
- Add PgBouncer (transaction mode, 500 client → 25 pool connections)
- Chat SSE stream via Redis pub/sub instead of 3s polling
- Optimistic UI in ChatPanel (messages appear before server confirms)
- Redis-based rate limiter (works across multiple app replicas)
- Prisma query optimization (select only needed fields)
- Chat message cache in Redis (10s TTL)
- Docker Compose: add redis, pgbouncer services with healthchecks
- Production: resource limits, 2 app replicas behind Traefik
- Update CLAUDE.md, README.md, .env.example, setup.sh

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

package.json

@@ -26,6 +26,7 @@
     "@types/react-dom": "^19.2.3",
     "bcryptjs": "^3.0.3",
     "better-auth": "^1.5.5",
+    "ioredis": "^5.10.1",
     "livekit-client": "^2.17.3",
     "livekit-server-sdk": "^2.15.0",
     "next": "^16.2.1",