Reduce integration test overhead (#32475)

In profiling integration tests, I found a couple places where per-test
overhead could be reduced:

* Avoiding disk IO by synchronizing instead of deleting & copying test
Git repository data. This saves ~100ms per test on my machine
* When flushing queues in `PrintCurrentTest`, invoke `FlushWithContext`
in a parallel.

---------

Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>

tests/integration/integration_test.go

@@ -400,8 +400,9 @@ func MakeRequest(t testing.TB, rw *RequestWrapper, expectedStatus int) *httptest
 	}
 	testWebRoutes.ServeHTTP(recorder, req)
 	if expectedStatus != NoExpectedStatus {
-		if !assert.EqualValues(t, expectedStatus, recorder.Code, "Request: %s %s", req.Method, req.URL.String()) {
+		if expectedStatus != recorder.Code {
 			logUnexpectedResponse(t, recorder)
+			require.Equal(t, expectedStatus, recorder.Code, "Request: %s %s", req.Method, req.URL.String())
 		}
 	}
 	return recorder