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
new Request(), IntStream.range(0, 3)
                    .mapToObj(shardId -> TestShardRouting.newShardRouting(TEST_INDEX, shardId, "node-id", true, ShardRoutingState.STARTED))
                    .toList(), "node-id"
            ),
            new TestTransportChannel(nodeResponseFuture),
            task
        );
        assertEquals(3, listeners.size());
        final var reachabilityChecker = new ReachabilityChecker();
        listeners.get(0).onResponse(reachabilityChecker.register(new ShardResult()));
        reachabilityChecker.checkReachable();
        TaskCancelHelper.cancel(task, "simulated");
        reachabilityChecker.ensureUnreachable();
        listeners.get(1).onResponse(reachabilityChecker.register(new ShardResult()));
        reachabilityChecker.ensureUnreachable();
        assertFalse(nodeResponseFuture.isDone());
        listeners.get(2).onResponse(reachabilityChecker.register(new ShardResult()));
        reachabilityChecker.ensureUnreachable();
        assertTrue(nodeResponseFuture.isDone());
        assertEquals(
            "task cancelled [simulated]",
            expectThrows(
                java.util.concurrent.ExecutionException.class,
                org.elasticsearch.tasks.TaskCancelledException.class,
                nodeResponseFuture::get
            ).getMessage()
        );
    }
}