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
public void testRequestsAreNotSentToFailedMaster() {
        Request request = new Request(TEST_INDEX);
        PlainActionFuture<Response> listener = new PlainActionFuture<>();
        DiscoveryNode masterNode = clusterService.state().nodes().getMasterNode();
        DiscoveryNodes.Builder builder = DiscoveryNodes.builder(clusterService.state().getNodes());
        builder.remove(masterNode.getId()).masterNodeId(null);
        setState(clusterService, ClusterState.builder(clusterService.state()).nodes(builder));
        action.doExecute(null, request, listener);
        Map<String, List<CapturingTransport.CapturedRequest>> capturedRequests = transport.getCapturedRequestsByTargetNodeAndClear();
        
        ShardsIterator shardIt = clusterService.state().routingTable().allShards(new String[] { TEST_INDEX });
        Set<String> set = new HashSet<>();
        for (ShardRouting shard : shardIt) {
            if (shard.currentNodeId().equals(masterNode.getId()) == false) {
                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());
        }
    }