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/internal/domain/errors.go

@@ -10,6 +10,7 @@ import "errors"
 var (
 	ErrJobNotFound    = errors.New("job not found")
 	ErrTaskNotFound   = errors.New("task not found")
+	ErrWorkerNotFound = errors.New("worker not found")
 	ErrLeaseConflict  = errors.New("task leased to another worker")
 	ErrStaleAttempt   = errors.New("attempt does not match lease")
 	ErrResultConflict = errors.New("different result already recorded")

coordinator/internal/domain/worker.go

@@ -0,0 +1,45 @@
+package domain
+
+import (
+	"time"
+
+	"github.com/google/uuid"
+)
+
+type WorkerStatus string
+
+const (
+	WorkerOnline  WorkerStatus = "online"
+	WorkerBusy    WorkerStatus = "busy"
+	WorkerOffline WorkerStatus = "offline"
+)
+
+// Worker is a registered process/machine allowed to claim tasks. Its
+// capabilities are the allowlisted workload names it can run; the coordinator
+// never hands it a task outside that set.
+type Worker struct {
+	ID              uuid.UUID
+	Name            string
+	Capabilities    []string
+	Status          WorkerStatus
+	LastHeartbeatAt time.Time
+	CreatedAt       time.Time
+	UpdatedAt       time.Time
+}
+
+// NewWorker registers a worker. A worker with no capabilities could never be
+// handed a task, so an empty set is rejected rather than silently stored.
+func NewWorker(name string, capabilities []string, now time.Time) (*Worker, error) {
+	if len(capabilities) == 0 {
+		return nil, ErrInvalidInput
+	}
+	return &Worker{
+		ID:              uuid.New(),
+		Name:            name,
+		Capabilities:    capabilities,
+		Status:          WorkerOnline,
+		LastHeartbeatAt: now,
+		CreatedAt:       now,
+		UpdatedAt:       now,
+	}, nil
+}