Three interrelated issues here:

- [ ] `TransportBroadcastByNodeAction` derivatives are typically executed via `NodeClient` which bypasses the `TransportService` and therefore does not respect (or even know about) the `executor` parameter which would fork. This means that the coordination work, including grouping all the shards by node, happens on the calling thread. When executed from the REST layer, that's a transport worker. This is #97916, but until that's fixed we need a workaround.

- [ ] The node-level responses are deserialised and processed on the receiving transport worker too.

- [ ] Several of these actions use `SAME` for their executor, bypassing the forking that _does_ exist today.

Relates #77466 
server/src/test/java/org/elasticsearch/action/support/broadcast/node/TransportBroadcastByNodeActionTests.java
set.add(shard.currentNodeId());
        }
        
        assertEquals(set.size(), capturedRequests.size());
        
        assertEquals(set, capturedRequests.keySet());
        for (Map.Entry<String, List<CapturingTransport.CapturedRequest>> entry : capturedRequests.entrySet()) {
            
            assertEquals(1, entry.getValue().size());
        }
    }
    public void testNoShardOperationsExecutedIfTaskCancelled() throws Exception {
        ShardsIterator shardIt = clusterService.state().routingTable().allShards(new String[] { TEST_INDEX });
        Set<ShardRouting> shards = new HashSet<>();
        String nodeId = shardIt.iterator().next().currentNodeId();
        for (ShardRouting shard : shardIt) {
            if (nodeId.equals(shard.currentNodeId())) {
                shards.add(shard);
            }
        }
        final TransportBroadcastByNodeAction<Request, Response, ShardResult>.BroadcastByNodeTransportRequestHandler handler =
            action.new BroadcastByNodeTransportRequestHandler();
        final PlainActionFuture<TransportResponse> future = PlainActionFuture.newFuture();
        TestTransportChannel channel = new TestTransportChannel(future);
        final CancellableTask cancellableTask = new CancellableTask(randomLong(), "transport", "action", "", null, emptyMap());
        TaskCancelHelper.cancel(cancellableTask, "simulated");
        handler.messageReceived(action.new NodeRequest(new Request(), new ArrayList<>(shards), nodeId), channel, cancellableTask);
        expectThrows(TaskCancelledException.class, future::actionGet);
        assertThat(action.getResults(), anEmptyMap());
    }