Fix flaky testClusterStateBatchedUpdates test (#10922)

Signed-off-by: Aman Khare <amkhar@amazon.com>
Co-authored-by: Aman Khare <amkhar@amazon.com>
(cherry picked from commit 44a9f18)
Signed-off-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>

server/src/test/java/org/opensearch/cluster/service/MasterServiceTests.java

@@ -487,6 +487,9 @@ public void onFailure(String source, Exception e) {
                     }
                 });
                 assertBusy(mockAppender::assertAllExpectationsMatched);
+                // verify stats values after state is published
+                assertEquals(1, clusterManagerService.getClusterStateStats().getUpdateSuccess());
+                assertEquals(0, clusterManagerService.getClusterStateStats().getUpdateFailed());
             }
         }
     }
@@ -691,9 +694,6 @@ public void clusterStateProcessed(String source, ClusterState oldState, ClusterS
                     submittedTasksPerThread.get(entry.getKey()).get()
                 );
             }
-            // verify stats values after state is published
-            assertEquals(1, clusterManagerService.getClusterStateStats().getUpdateSuccess());
-            assertEquals(0, clusterManagerService.getClusterStateStats().getUpdateFailed());
         }
     }