Remove Redundant use of Cancellable Threads in PeerRecoveryTargetService (#65119)

The transport request sending call is completely async and never throws at this point
(all exceptions are caught and passed to the transport handler) making this use of cancellable
threads redundant.

server/src/main/java/org/elasticsearch/indices/recovery/PeerRecoveryTargetService.java

@@ -174,7 +174,6 @@ public class PeerRecoveryTargetService implements IndexEventListener {
         final TransportRequest requestToSend;
         final StartRecoveryRequest startRequest;
         final RecoveryState.Timer timer;
-        CancellableThreads cancellableThreads;
         try (RecoveryRef recoveryRef = onGoingRecoveries.getRecovery(recoveryId)) {
             if (recoveryRef == null) {
                 logger.trace("not running recovery with id [{}] - can not find it (probably finished)", recoveryId);
@@ -182,7 +181,6 @@ public class PeerRecoveryTargetService implements IndexEventListener {
             }
             final RecoveryTarget recoveryTarget = recoveryRef.target();
             timer = recoveryTarget.state().getTimer();
-            cancellableThreads = recoveryTarget.cancellableThreads();
             if (preExistingRequest == null) {
                 try {
                     final IndexShard indexShard = recoveryTarget.indexShard();
@@ -211,22 +209,8 @@ public class PeerRecoveryTargetService implements IndexEventListener {
                 logger.trace("{} reestablishing recovery from {}", startRequest.shardId(), startRequest.sourceNode());
             }
         }
-        RecoveryResponseHandler responseHandler = new RecoveryResponseHandler(startRequest, timer);
-
-        try {
-            cancellableThreads.executeIO(() ->
-                // we still execute under cancelableThreads here to ensure we interrupt any blocking call to the network if any
-                // on the underlying transport. It's unclear if we need this here at all after moving to async execution but
-                // the issues that a missing call to this could cause are sneaky and hard to debug. If we don't need it on this
-                // call we can potentially remove it altogether which we should do it in a major release only with enough
-                // time to test. This shoudl be done for 7.0 if possible
-                transportService.sendRequest(startRequest.sourceNode(), actionName, requestToSend, responseHandler)
-            );
-        } catch (CancellableThreads.ExecutionCancelledException e) {
-            logger.trace("recovery cancelled", e);
-        } catch (Exception e) {
-            responseHandler.onException(e);
-        }
+        transportService.sendRequest(startRequest.sourceNode(), actionName, requestToSend,
+                new RecoveryResponseHandler(startRequest, timer));
     }
 
     /**
@@ -583,10 +567,6 @@ public class PeerRecoveryTargetService implements IndexEventListener {
 
         @Override
         public void handleException(TransportException e) {
-            onException(e);
-        }
-
-        private void onException(Exception e) {
             if (logger.isTraceEnabled()) {
                 logger.trace(() -> new ParameterizedMessage(
                     "[{}][{}] Got exception on recovery", request.shardId().getIndex().getName(),