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/api/requests.http

@@ -10,7 +10,7 @@
 @token = change-me
 @worker = worker-1
 
-### Health — the only unauthenticated endpoint
+### Readiness — the only unauthenticated endpoint (probes the database)
 GET {{host}}/health
 
 ### Auth check — no token must be rejected with 401
@@ -19,6 +19,21 @@ Content-Type: application/json
 
 { "worker_id": "{{worker}}" }
 
+### 0. Register a worker (201)
+# @name register
+POST {{host}}/workers/register
+Authorization: Bearer {{token}}
+Content-Type: application/json
+
+{
+  "name": "lab-worker-01",
+  "capabilities": ["similarity_search"],
+  "cpu_count": 8,
+  "memory_mb": 16384
+}
+
+@workerId = {{register.response.body.worker_id}}
+
 ### 1. Create a job and its chunks (201)
 # The coordinator splits the submission into one task per chunk, transactionally.
 # @name createJob
@@ -48,7 +63,8 @@ Content-Type: application/json
 
 {
   "worker_id": "{{worker}}",
-  "workloads": ["similarity_search"]
+  "capabilities": ["similarity_search"],
+  "max_concurrency": 1
 }
 
 @taskId = {{claim.response.body.task_id}}