fix: Calculate stale task count from heartbeat age

backend/src/tasks/task-service.ts

@@ -615,15 +615,25 @@ class TaskService {
       return counts;
     }
 
+    // Get counts by status, with stale calculated from running tasks with old heartbeats
     const result = await pool.query(
-      `SELECT status, COUNT(*) as count
+      `SELECT
+         CASE
+           WHEN status IN ('running', 'claimed')
+             AND last_heartbeat_at < NOW() - INTERVAL '2 minutes'
+           THEN 'stale'
+           ELSE status
+         END as effective_status,
+         COUNT(*) as count
        FROM worker_tasks
-       GROUP BY status`
+       GROUP BY effective_status`
     );
 
     for (const row of result.rows) {
-      const typedRow = row as { status: TaskStatus; count: string };
+      const typedRow = row as { effective_status: TaskStatus; count: string };
-      counts[typedRow.status] = parseInt(typedRow.count, 10);
+      if (typedRow.effective_status in counts) {
+        counts[typedRow.effective_status] = parseInt(typedRow.count, 10);
+      }
     }
 
     return counts;