Add PostgreSQL dual writes and room metrics

[coder13]

Summary

• add a PostgreSQL 17 sidecar and define the app and analytics schemas in Prisma
• manage schema history with Prisma Migrate and run prisma migrate deploy as a one-shot production Compose service
• mirror new users, rooms, participant state, attempts, solves, and explicit room deletion into PostgreSQL with deterministic UUIDs and timestamp-guarded upserts
• store solve penalties in dedicated boolean columns and index user history by creation time plus solve ID for stable cursor pagination
• mirror only dirty room participants, attempts, and results during live saves instead of replaying the complete room history
• remove obsolete PostgreSQL attempts when a MongoDB room changes events, while retaining full snapshot writes for explicit backfills
• collect pseudonymous room lifecycle, solve-count, and authentication-failure events in MongoDB and PostgreSQL with configurable retention
• enforce Prisma schema validation, migration application, and database drift checks in CI
• stop client analytics page views from including query strings

Why

This starts ingesting durable solve and analytics data into PostgreSQL while keeping the existing MongoDB-backed application behavior unchanged. Prisma provides the canonical PostgreSQL schema and migration history, while pg remains the small runtime layer for PostgreSQL-specific dual-write upserts.

Incremental writes prevent solve ingestion from becoming quadratic as room history grows. Normalized penalty fields keep solve statistics queryable without JSON extraction, and unchanged same-timestamp retries are true no-ops to reduce unnecessary PostgreSQL churn.

Rollout and privacy

• MongoDB remains the source of truth and all application reads still use MongoDB.
• PostgreSQL writes are fail-open during migration: failures are logged without failing the corresponding MongoDB operation.
• This handles new writes only. A separate batched backfill job is still needed before any cutover.
• OAuth access tokens are not copied.
• Analytics identifiers are HMAC-pseudonymized, and metric events exclude names, email addresses, WCA IDs, room secrets, chat, scrambles, and solve times.
• Mirroring can be disabled with POSTGRES_ENABLED=false; metrics can be disabled independently with METRICS_ENABLED=false.
• DIRECT_DATABASE_URL can provide a direct migration connection when runtime DATABASE_URL traffic is pooled.

Validation

• yarn lint
• yarn test — 45 tests passed
• yarn build
• prisma validate
• Prisma migrations applied to PostgreSQL 17 with zero schema drift
• live incremental solve and participant dual-write smoke test
• live room-event attempt replacement smoke test
• production migration container build and execution
• production and development Compose validation
• production dependency audit; only the pre-existing low-severity cookie advisory remains