feat(coordinator): worker registry, API contract, logging & DB retry

Align the coordinator with the master PLAN.md (CTX-00, CTX-04) and harden
process startup.

- CTX-00: freeze docs/api-contract.md as the v1 source of truth for the
  Go coordinator and Python worker.
- CTX-04: worker registry — workers table (migration 0002), domain.Worker,
  RegisterWorker use case, WorkerRepository, and POST /workers/register.
- Contract alignment: claim uses `capabilities` (was `workloads`),
  COORDINATOR_TOKEN env (WORKER_AUTH_TOKEN kept as fallback), and
  GET /health now reports database readiness (503 when the DB is down).
- Logging: logs are teed to stdout and an optional rotated file (LOG_FILE)
  via lumberjack, so they survive a container rebuild.
- Startup resilience: the initial DB connection is retried with backoff,
  so the coordinator waits for Postgres to boot instead of crash-looping.

coordinator/.gitignore

@@ -2,3 +2,4 @@
 /bin/
 .env
 *.out
+/logs/