Fix Flaky Test SpecificClusterManagerNodesIT.testElectOnlyBetweenClusterManagerNodes

Signed-off-by: kkewwei <kkewwei@163.com>

Author: kkewwei

server/src/internalClusterTest/java/org/opensearch/cluster/SpecificClusterManagerNodesIT.java

@@ -224,19 +224,6 @@ public void testElectOnlyBetweenClusterManagerNodes() throws Exception {
                 .getName(),
             equalTo(clusterManagerNodeName)
         );
-        assertThat(
-            internalCluster().nonClusterManagerClient()
-                .admin()
-                .cluster()
-                .prepareState()
-                .execute()
-                .actionGet()
-                .getState()
-                .nodes()
-                .getClusterManagerNode()
-                .getName(),
-            equalTo(clusterManagerNodeName)
-        );
         assertThat(
             internalCluster().clusterManagerClient()
                 .admin()
@@ -254,8 +241,10 @@ public void testElectOnlyBetweenClusterManagerNodes() throws Exception {
         logger.info("--> closing cluster-manager node (1)");
         client().execute(AddVotingConfigExclusionsAction.INSTANCE, new AddVotingConfigExclusionsRequest(clusterManagerNodeName)).get();
         // removing the cluster-manager from the voting configuration immediately triggers the cluster-manager to step down
-        assertBusy(() -> {
-            assertThat(
+
+        // make sure `nextClusterManagerEligableNodeName` has been elected as the new cluster-manager
+        waitUntil(
+            () -> nextClusterManagerEligableNodeName.equals(
                 internalCluster().nonClusterManagerClient()
                     .admin()
                     .cluster()
@@ -265,23 +254,24 @@ public void testElectOnlyBetweenClusterManagerNodes() throws Exception {
                     .getState()
                     .nodes()
                     .getClusterManagerNode()
-                    .getName(),
-                equalTo(nextClusterManagerEligableNodeName)
-            );
-            assertThat(
-                internalCluster().clusterManagerClient()
-                    .admin()
-                    .cluster()
-                    .prepareState()
-                    .execute()
-                    .actionGet()
-                    .getState()
-                    .nodes()
-                    .getClusterManagerNode()
-                    .getName(),
-                equalTo(nextClusterManagerEligableNodeName)
-            );
-        });
+                    .getName()
+            )
+        );
+
+        assertThat(
+            internalCluster().clusterManagerClient()
+                .admin()
+                .cluster()
+                .prepareState()
+                .execute()
+                .actionGet()
+                .getState()
+                .nodes()
+                .getClusterManagerNode()
+                .getName(),
+            equalTo(nextClusterManagerEligableNodeName)
+        );
+
         internalCluster().stopRandomNode(InternalTestCluster.nameFilter(clusterManagerNodeName));
         assertThat(
             internalCluster().nonClusterManagerClient()