Fix testBatchedUpdateSummaryLogging (#93087)

The `MasterService` emits some log messages after notifying all its
listeners, which means we cannot shut the mock log appender down as soon
as the listeners are all notified. Instead, we must drain the executor
service within the `MasterService` by shutting the whole service down
first.

Closes #93069

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

@@ -444,7 +444,7 @@ public class MasterServiceTests extends ESTestCase {
             )
         );
 
-        try (var masterService = createMasterService(true); var ignored = mockAppender.capturing(MasterService.class)) {
+        try (var ignored = mockAppender.capturing(MasterService.class); var masterService = createMasterService(true)) {
             masterService.submitUnbatchedStateUpdateTask("test1", new ClusterStateUpdateTask() {
                 @Override
                 public ClusterState execute(ClusterState currentState) {
@@ -1172,13 +1172,13 @@ public class MasterServiceTests extends ESTestCase {
             .put(Node.NODE_NAME_SETTING.getKey(), "test_node")
             .build();
         try (
+            var ignored = mockAppender.capturing(MasterService.class);
             MasterService masterService = new MasterService(
                 settings,
                 new ClusterSettings(Settings.EMPTY, ClusterSettings.BUILT_IN_CLUSTER_SETTINGS),
                 threadPool,
                 new TaskManager(settings, threadPool, emptySet())
-            );
-            var ignored = mockAppender.capturing(MasterService.class)
+            )
         ) {
             final DiscoveryNode localNode = new DiscoveryNode(
                 "node1",
@@ -1803,7 +1803,7 @@ public class MasterServiceTests extends ESTestCase {
     )
     public void testBatchedUpdateSummaryLogging() throws Exception {
         MockLogAppender mockAppender = new MockLogAppender();
-        try (var masterService = createMasterService(true); var ignored = mockAppender.capturing(MasterService.class)) {
+        try (var ignored = mockAppender.capturing(MasterService.class); var masterService = createMasterService(true)) {
 
             final var barrier = new CyclicBarrier(2);
             final var blockingTask = new ClusterStateUpdateTask() {