Flow improvements.

modules/web_app.py

@@ -977,7 +977,13 @@ def run_status(id):
             if os.path.exists(temp_log):
                 with open(temp_log, 'r') as f: log_content = f.read()
         
-    response = {"status": run.status, "log": log_content, "cost": run.cost, "percent": run.progress}
+    response = {
+        "status": run.status, 
+        "log": log_content, 
+        "cost": run.cost, 
+        "percent": run.progress,
+        "start_time": run.start_time.timestamp() if run.start_time else None
+    }
     
     if last_log:
         response["progress"] = {