Rehearse and execute the modernized production rollout with a tested rollback

## Goal

Ship the Node 22, Vite, MongoDB 7, Redis, Docker Compose, and PostgreSQL dual-write stack without making production the first full migration test.

## Acceptance criteria

- [ ] Complete the integrated release candidate in #173.
- [ ] Capture a fresh MongoDB backup and successfully restore it into a non-production rehearsal environment.
- [ ] Rehearse the Compose deployment, Prisma `migrate deploy`, API/socket startup, and health checks using production-shaped configuration.
- [ ] Verify login, room create/join/rejoin, spectating, result submission/editing, room expiry, and Redis-backed multi-process Socket.IO behavior.
- [ ] Configure PostgreSQL credentials, `METRICS_HASH_SECRET`, retention, TLS/CA settings where applicable, and confirm secrets are not logged.
- [ ] Define rollback triggers and rehearse rollback to the previous app revision without deleting or downgrading data.
- [ ] Promote the reviewed `dev → master` release and monitor API/socket errors, auth failures, room events, PostgreSQL write failures, and resource use.
- [ ] Record the deployed commit and post-deploy verification results.

## References

- `README_DEPLOYMENT.md`
- PR #171
- #173
- #177

README_DEPLOYMENT.md と #173 の統合されたリリース候補から始め、その後 PR #171 と #177 をレビューします。非本番環境で、バックアップの復元、Compose のデプロイ、マイグレーション、ヘルスチェック、アプリケーションフロー、シークレット、ロールバックをリハーサルします。レビュー済みの dev → master リリースがプロモートされ、監視され、そのコミットと検証結果とともに文書化されていれば完了です。

索引モデルが issue の本文から書いたものです。