Add AI queue backlog metrics

internal/store/store.go

@@ -713,7 +713,47 @@ ORDER BY owner_service, task_type, model_profile
 		}
 		out.Stages = append(out.Stages, stat)
 	}
-	return out, stageRows.Err()
+	if err := stageRows.Err(); err != nil {
+		return nil, err
+	}
+
+	backlogRows, err := s.pool.Query(ctx, `
+SELECT owner_service,
+       task_type,
+       model_profile,
+       count(*) FILTER (WHERE status = 'pending') AS pending,
+       count(*) FILTER (WHERE status = 'running') AS running,
+       COALESCE(EXTRACT(EPOCH FROM (NOW() - MIN(scheduled_at) FILTER (WHERE status = 'pending')))::bigint, 0) AS oldest_pending_age_seconds,
+       MIN(scheduled_at) FILTER (WHERE status = 'pending') AS oldest_pending_scheduled_at
+FROM ai_jobs
+WHERE status IN ('pending', 'running')
+GROUP BY owner_service, task_type, model_profile
+ORDER BY pending DESC, running DESC, owner_service, task_type, model_profile
+`)
+	if err != nil {
+		return nil, err
+	}
+	defer backlogRows.Close()
+	for backlogRows.Next() {
+		var stat model.BacklogStat
+		var oldestPendingScheduledAt *time.Time
+		if err := backlogRows.Scan(
+			&stat.OwnerService,
+			&stat.TaskType,
+			&stat.ModelProfile,
+			&stat.Pending,
+			&stat.Running,
+			&stat.OldestPendingAgeSeconds,
+			&oldestPendingScheduledAt,
+		); err != nil {
+			return nil, err
+		}
+		if oldestPendingScheduledAt != nil {
+			stat.OldestPendingScheduledAt = oldestPendingScheduledAt.UTC().Format(time.RFC3339)
+		}
+		out.Backlog = append(out.Backlog, stat)
+	}
+	return out, backlogRows.Err()
 }
 
 func scanJobSummary(row pgx.Row) (*model.JobSummary, error) {