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/storage/postgres/worker_repo.go

@@ -0,0 +1,65 @@
+package postgres
+
+import (
+	"context"
+	"errors"
+	"fmt"
+
+	"github.com/google/uuid"
+	"github.com/jackc/pgx/v5"
+	"github.com/jackc/pgx/v5/pgxpool"
+
+	"github.com/emil28092005/SciMesh/coordinator/internal/domain"
+)
+
+// WorkerRepo implements usecase.WorkerRepository.
+type WorkerRepo struct {
+	pool *pgxpool.Pool
+}
+
+func NewWorkerRepo(pool *pgxpool.Pool) *WorkerRepo {
+	return &WorkerRepo{pool: pool}
+}
+
+const workerColumns = `id, name, capabilities, status, last_heartbeat_at, created_at, updated_at`
+
+const insertWorkerSQL = `
+INSERT INTO workers (` + workerColumns + `)
+VALUES ($1, $2, $3, $4, $5, $6, $7)`
+
+func (r *WorkerRepo) Insert(ctx context.Context, w *domain.Worker) error {
+	// capabilities is a jsonb column; pgx marshals the []string to a JSON array.
+	_, err := conn(ctx, r.pool).Exec(ctx, insertWorkerSQL,
+		w.ID, w.Name, w.Capabilities, string(w.Status),
+		w.LastHeartbeatAt, w.CreatedAt, w.UpdatedAt)
+	if err != nil {
+		return fmt.Errorf("insert worker: %w", err)
+	}
+	return nil
+}
+
+const getWorkerSQL = `SELECT ` + workerColumns + ` FROM workers WHERE id = $1`
+
+func (r *WorkerRepo) Get(ctx context.Context, id uuid.UUID) (*domain.Worker, error) {
+	w, err := scanWorker(conn(ctx, r.pool).QueryRow(ctx, getWorkerSQL, id))
+	if errors.Is(err, pgx.ErrNoRows) {
+		return nil, domain.ErrWorkerNotFound
+	}
+	if err != nil {
+		return nil, fmt.Errorf("get worker: %w", err)
+	}
+	return w, nil
+}
+
+func scanWorker(row pgx.Row) (*domain.Worker, error) {
+	var (
+		w      domain.Worker
+		status string
+	)
+	if err := row.Scan(&w.ID, &w.Name, &w.Capabilities, &status,
+		&w.LastHeartbeatAt, &w.CreatedAt, &w.UpdatedAt); err != nil {
+		return nil, err
+	}
+	w.Status = domain.WorkerStatus(status)
+	return &w, nil
+}