Add wait for remote start for the test (#131124)

Author: smalyshev

muted-tests.yml

@@ -341,9 +341,6 @@ tests:
 - class: org.elasticsearch.xpack.test.rest.XPackRestIT
  method: test {p0=ml/data_frame_analytics_cat_apis/Test cat data frame analytics all jobs with header}
  issue: https://github.com/elastic/elasticsearch/issues/127625
-- class: org.elasticsearch.xpack.search.CrossClusterAsyncSearchIT
- method: testCancellationViaTimeoutWithAllowPartialResultsSetToFalse
- issue: https://github.com/elastic/elasticsearch/issues/127096
 - class: org.elasticsearch.xpack.ccr.action.ShardFollowTaskReplicationTests
  method: testChangeFollowerHistoryUUID
  issue: https://github.com/elastic/elasticsearch/issues/127680

x-pack/plugin/async-search/src/internalClusterTest/java/org/elasticsearch/xpack/search/CrossClusterAsyncSearchIT.java

@@ -1778,6 +1778,7 @@ public void testCancellationViaTimeoutWithAllowPartialResultsSetToFalse() throws
  }
 
  SearchListenerPlugin.waitLocalSearchStarted();
+ SearchListenerPlugin.waitRemoteSearchStarted();
 
  // ensure tasks are present on both clusters and not cancelled
  try {