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/main/java/org/elasticsearch/action/support/broadcast/node/TransportBroadcastByNodeAction.java
private final Request indicesLevelRequest;
        private final List<ShardRouting> shards;
        private final String nodeId;
        NodeRequest(StreamInput in) throws IOException {
            super(in);
            indicesLevelRequest = readRequestFrom(in);
            shards = in.readList(ShardRouting::new);
            nodeId = in.readString();
        }
        NodeRequest(Request indicesLevelRequest, List<ShardRouting> shards, String nodeId) {
            this.indicesLevelRequest = indicesLevelRequest;
            this.shards = shards;
            this.nodeId = nodeId;
        }