Remove calls to deprecated MessageLoop methods in ios.

ios/chrome/browser/browser_state/test_chrome_browser_state.mm

Index: ios/chrome/browser/browser_state/test_chrome_browser_state.mm
diff --git a/ios/chrome/browser/browser_state/test_chrome_browser_state.mm b/ios/chrome/browser/browser_state/test_chrome_browser_state.mm
index 1e5dd33a4fce4a0221580300ac34128f77e84d71..37ecd8e95c61617840fd1e3394385da3bc8d6acb 100644
--- a/ios/chrome/browser/browser_state/test_chrome_browser_state.mm
+++ b/ios/chrome/browser/browser_state/test_chrome_browser_state.mm
@@ -360,9 +360,10 @@ void TestChromeBrowserState::DestroyHistoryService() {
   if (!history_service)
     return;
 
+  base::RunLoop run_loop;
+
   history_service->ClearCachedDataForContextID(0);
-  history_service->SetOnBackendDestroyTask(
-      base::MessageLoop::QuitWhenIdleClosure());
+  history_service->SetOnBackendDestroyTask(run_loop.QuitWhenIdleClosure());
   history_service->Shutdown();
   history_service = nullptr;
 
@@ -374,13 +375,7 @@ void TestChromeBrowserState::DestroyHistoryService() {
   // moving to the next test. Note: if this never terminates, somebody is
   // probably leaking a reference to the history backend, so it never calls
   // our destroy task.
-  base::MessageLoop::current()->Run();
-
-  // Make sure we don't have any event pending that could disrupt the next
-  // test.
-  base::ThreadTaskRunnerHandle::Get()->PostTask(
-      FROM_HERE, base::MessageLoop::QuitWhenIdleClosure());
-  base::MessageLoop::current()->Run();
+  run_loop.Run();
 }
 
 syncable_prefs::TestingPrefServiceSyncable*