Wrap async ql task execution in new tracing context (#89029)

Part of #84369. Split out from #88443. This PR wraps parts logic in
`AsyncTaskManagementService` in a new tracing context. This is
necessary so that a tracing implementation can use the thread context
to propagate tracing headers, but without the code attempting to set the
same key twice in the thread context, which is illegal.

x-pack/plugin/ql/src/main/java/org/elasticsearch/xpack/ql/async/AsyncTaskManagementService.java

@@ -170,20 +170,22 @@ public void asyncExecute(
         ActionListener<Response> listener
     ) {
         String nodeId = clusterService.localNode().getId();
-        @SuppressWarnings("unchecked")
-        T searchTask = (T) taskManager.register("transport", action + "[a]", new AsyncRequestWrapper(request, nodeId));
-        boolean operationStarted = false;
-        try {
-            operation.execute(
-                request,
-                searchTask,
-                wrapStoringListener(searchTask, waitForCompletionTimeout, keepAlive, keepOnCompletion, listener)
-            );
-            operationStarted = true;
-        } finally {
-            // If we didn't start operation for any reason, we need to clean up the task that we have created
-            if (operationStarted == false) {
-                taskManager.unregister(searchTask);
+        try (var ignored = threadPool.getThreadContext().newTraceContext()) {
+            @SuppressWarnings("unchecked")
+            T searchTask = (T) taskManager.register("transport", action + "[a]", new AsyncRequestWrapper(request, nodeId));
+            boolean operationStarted = false;
+            try {
+                operation.execute(
+                    request,
+                    searchTask,
+                    wrapStoringListener(searchTask, waitForCompletionTimeout, keepAlive, keepOnCompletion, listener)
+                );
+                operationStarted = true;
+            } finally {
+                // If we didn't start operation for any reason, we need to clean up the task that we have created
+                if (operationStarted == false) {
+                    taskManager.unregister(searchTask);
+                }
             }
         }
     }