[router] Fix Flaky test_circuit_breaker_opens_and_recovers (#13164)

Author: XinyueZhang369

sgl-router/py_test/integration_mock/test_circuit_breaker.py

@@ -32,8 +32,21 @@ def post_once():
             timeout=3,
         )
 
-    saw_503 = False
+    # should see 500 when worker actually starts, before that should see 503
+    saw_500 = False
     for _ in range(8):
+        r = post_once()
+        if r.status_code == 500:
+            # Worker starts, continue to circuit breaker test
+            saw_500 = True
+            break
+        assert (
+            r.status_code == 503
+        ), "Should only see 503 when waiting for worker to start"
+    assert saw_500, "Worker didn't start after 8 requests"
+
+    saw_503 = False
+    for _ in range(4):
         r = post_once()
         if r.status_code == 503:
             saw_503 = True