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
action.doExecute(null, request, listener);
            fail("expected ClusterBlockException");
        } catch (ClusterBlockException expected) {
            assertEquals("blocked by: [SERVICE_UNAVAILABLE/1/test-block];", expected.getMessage());
        }
    }
    public void testRequestBlock() {
        Request request = new Request(TEST_INDEX);
        PlainActionFuture<Response> listener = new PlainActionFuture<>();
        ClusterBlocks.Builder block = ClusterBlocks.builder()
            .addIndexBlock(
                TEST_INDEX,
                new ClusterBlock(1, "test-block", false, true, false, RestStatus.SERVICE_UNAVAILABLE, ClusterBlockLevel.ALL)
            );
        setState(clusterService, ClusterState.builder(clusterService.state()).blocks(block));
        try {
            action.doExecute(null, request, listener);
            fail("expected ClusterBlockException");
        } catch (ClusterBlockException expected) {
            assertEquals("index [" + TEST_INDEX + "] blocked by: [SERVICE_UNAVAILABLE/1/test-block];", expected.getMessage());
        }
    }
    public void testOneRequestIsSentToEachNodeHoldingAShard() {
        Request request = new Request(TEST_INDEX);
        PlainActionFuture<Response> listener = new PlainActionFuture<>();
        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) {