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/migrations/0002_workers.down.sql

@@ -0,0 +1,6 @@
+BEGIN;
+
+DROP TABLE IF EXISTS workers;
+DROP TYPE IF EXISTS worker_status;
+
+COMMIT;

coordinator/migrations/0002_workers.up.sql

@@ -0,0 +1,20 @@
+BEGIN;
+
+CREATE TYPE worker_status AS ENUM ('online','busy','offline');
+
+-- A registered process/machine that can claim tasks. Registration returns the
+-- id; liveness is tracked by last_heartbeat_at.
+CREATE TABLE workers (
+    id                uuid          PRIMARY KEY,
+    name              text          NOT NULL DEFAULT '',
+    capabilities      jsonb         NOT NULL DEFAULT '[]'::jsonb,
+    status            worker_status NOT NULL DEFAULT 'online',
+    last_heartbeat_at timestamptz   NOT NULL DEFAULT now(),
+    created_at        timestamptz   NOT NULL DEFAULT now(),
+    updated_at        timestamptz   NOT NULL DEFAULT now()
+);
+
+-- Liveness sweep: find workers that have gone quiet.
+CREATE INDEX ix_workers_liveness ON workers (status, last_heartbeat_at);
+
+COMMIT;