diff --git a/server/src/main/java/org/elasticsearch/cluster/coordination/CoordinationDiagnosticsService.java b/server/src/main/java/org/elasticsearch/cluster/coordination/CoordinationDiagnosticsService.java
index b474cb67772a5..82b85329d9dbd 100644
--- a/server/src/main/java/org/elasticsearch/cluster/coordination/CoordinationDiagnosticsService.java
+++ b/server/src/main/java/org/elasticsearch/cluster/coordination/CoordinationDiagnosticsService.java
@@ -991,20 +991,16 @@ private <R extends ActionResponse, T> Scheduler.Cancellable sendTransportRequest
                 logger.trace("Opened connection to {}, making transport request", masterEligibleNode);
                 // If we don't get a response in 10 seconds that is a failure worth capturing on its own:
                 final TimeValue transportTimeout = TimeValue.timeValueSeconds(10);
-                try {
-                    transportService.sendRequest(
-                        masterEligibleNode,
-                        transportActionType.name(),
-                        transportActionRequest,
-                        TransportRequestOptions.timeout(transportTimeout),
-                        new ActionListenerResponseHandler<>(
-                            ActionListener.runBefore(fetchRemoteResultListener, () -> Releasables.close(releasable)),
-                            transportActionType.getResponseReader()
-                        )
-                    );
-                } catch (Exception e) {
-                    responseConsumer.accept(responseTransformationFunction.apply(null, e));
-                }
+                transportService.sendRequest(
+                    masterEligibleNode,
+                    transportActionType.name(),
+                    transportActionRequest,
+                    TransportRequestOptions.timeout(transportTimeout),
+                    new ActionListenerResponseHandler<>(
+                        ActionListener.runBefore(fetchRemoteResultListener, () -> Releasables.close(releasable)),
+                        transportActionType.getResponseReader()
+                    )
+                );
             }
         }, e -> {
             logger.warn("Exception connecting to master masterEligibleNode", e);
diff --git a/server/src/main/java/org/elasticsearch/cluster/coordination/PublicationTransportHandler.java b/server/src/main/java/org/elasticsearch/cluster/coordination/PublicationTransportHandler.java
index 048b2e6665102..67dddfa6c247b 100644
--- a/server/src/main/java/org/elasticsearch/cluster/coordination/PublicationTransportHandler.java
+++ b/server/src/main/java/org/elasticsearch/cluster/coordination/PublicationTransportHandler.java
@@ -423,24 +423,18 @@ private void sendClusterState(
                 listener.onFailure(new IllegalStateException("serialized cluster state released before transmission"));
                 return;
             }
-            try {
-                transportService.sendChildRequest(
-                    destination,
-                    PUBLISH_STATE_ACTION_NAME,
-                    new BytesTransportRequest(bytes, destination.getVersion()),
-                    task,
-                    STATE_REQUEST_OPTIONS,
-                    new ActionListenerResponseHandler<>(
-                        ActionListener.runAfter(listener, bytes::decRef),
-                        PublishWithJoinResponse::new,
-                        ThreadPool.Names.CLUSTER_COORDINATION
-                    )
-                );
-            } catch (Exception e) {
-                assert false : e;
-                logger.warn(() -> format("error sending cluster state to %s", destination), e);
-                listener.onFailure(e);
-            }
+            transportService.sendChildRequest(
+                destination,
+                PUBLISH_STATE_ACTION_NAME,
+                new BytesTransportRequest(bytes, destination.getVersion()),
+                task,
+                STATE_REQUEST_OPTIONS,
+                new ActionListenerResponseHandler<>(
+                    ActionListener.runAfter(listener, bytes::decRef),
+                    PublishWithJoinResponse::new,
+                    ThreadPool.Names.CLUSTER_COORDINATION
+                )
+            );
         }
 
         @Override
diff --git a/server/src/main/java/org/elasticsearch/transport/TransportService.java b/server/src/main/java/org/elasticsearch/transport/TransportService.java
index 3a30cbb433506..1b7fe6b615073 100644
--- a/server/src/main/java/org/elasticsearch/transport/TransportService.java
+++ b/server/src/main/java/org/elasticsearch/transport/TransportService.java
@@ -716,9 +716,15 @@ public final <T extends TransportResponse> void sendRequest(
         final Transport.Connection connection;
         try {
             connection = getConnection(node);
-        } catch (final NodeNotConnectedException ex) {
-            // the caller might not handle this so we invoke the handler
-            handler.handleException(ex);
+        } catch (TransportException transportException) {
+            // should only be a NodeNotConnectedException in practice, but handle all cases anyway to be sure
+            assert transportException instanceof NodeNotConnectedException : transportException;
+            handleSendRequestException(handler, transportException);
+            return;
+        } catch (Exception exception) {
+            // shouldn't happen in practice, but handle it anyway to be sure
+            assert false : exception;
+            handleSendRequestException(handler, new SendRequestTransportException(node, action, exception));
             return;
         }
         sendRequest(connection, action, request, options, handler);
@@ -776,25 +782,25 @@ public final <T extends TransportResponse> void sendRequest(
                 delegate = handler;
             }
             asyncSender.sendRequest(connection, action, request, options, delegate);
-        } catch (final Exception ex) {
-            handleSendRequestException(connection, action, handler, ex);
+        } catch (TransportException transportException) {
+            handleSendRequestException(handler, transportException);
+        } catch (Exception exception) {
+            handleSendRequestException(handler, new SendRequestTransportException(connection.getNode(), action, exception));
         }
     }
 
-    private <T extends TransportResponse> void handleSendRequestException(
-        Transport.Connection connection,
-        String action,
+    private static <T extends TransportResponse> void handleSendRequestException(
         TransportResponseHandler<T> handler,
-        Exception ex
+        TransportException transportException
     ) {
-        // the caller might not handle this so we invoke the handler
-        final TransportException te;
-        if (ex instanceof TransportException tex) {
-            te = tex;
-        } else {
-            te = new SendRequestTransportException(connection.getNode(), action, ex);
+        try {
+            handler.handleException(transportException);
+        } catch (Exception innerException) {
+            // should not happen
+            innerException.addSuppressed(transportException);
+            logger.error("unexpected exception from handler.handleException", innerException);
+            assert false : innerException;
         }
-        handler.handleException(te);
     }
 
     /**
@@ -820,9 +826,15 @@ public final <T extends TransportResponse> void sendChildRequest(
         final Transport.Connection connection;
         try {
             connection = getConnection(node);
-        } catch (final NodeNotConnectedException ex) {
-            // the caller might not handle this so we invoke the handler
-            handler.handleException(ex);
+        } catch (TransportException transportException) {
+            // should only be a NodeNotConnectedException in practice, but handle all cases anyway to be sure
+            assert transportException instanceof NodeNotConnectedException : transportException;
+            handleSendRequestException(handler, transportException);
+            return;
+        } catch (Exception exception) {
+            // shouldn't happen in practice, but handle it anyway to be sure
+            assert false : exception;
+            handleSendRequestException(handler, new SendRequestTransportException(node, action, exception));
             return;
         }
         sendChildRequest(connection, action, request, parentTask, options, handler);
diff --git a/test/framework/src/main/java/org/elasticsearch/transport/AbstractSimpleTransportTestCase.java b/test/framework/src/main/java/org/elasticsearch/transport/AbstractSimpleTransportTestCase.java
index b823a2b3f8b7c..a0c826dacbbee 100644
--- a/test/framework/src/main/java/org/elasticsearch/transport/AbstractSimpleTransportTestCase.java
+++ b/test/framework/src/main/java/org/elasticsearch/transport/AbstractSimpleTransportTestCase.java
@@ -3176,11 +3176,7 @@ public static <T extends TransportResponse> Future<T> submitRequest(
         responseListener.whenComplete(handler::handleResponse, e -> handler.handleException((TransportException) e));
         final PlainActionFuture<T> future = PlainActionFuture.newFuture();
         responseListener.addListener(future);
-        try {
-            transportService.sendRequest(node, action, request, options, futureHandler);
-        } catch (NodeNotConnectedException ex) {
-            futureHandler.handleException(ex);
-        }
+        transportService.sendRequest(node, action, request, options, futureHandler);
         return future;
     }
 }