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/admin/indices/stats/ShardStats.java
searchIdleTime
        );
    }
    /**
     * The shard routing information (cluster wide shard state).
     */
    public ShardRouting getShardRouting() {
        return this.shardRouting;
    }
    public CommonStats getStats() {
        return this.commonStats;
    }
    @Nullable
    public CommitStats getCommitStats() {
        return this.commitStats;
    }
    @Nullable
    public SeqNoStats getSeqNoStats() {
        return this.seqNoStats;
    }
    /**
     * Gets the current retention lease stats.
     *
     * @return the current retention lease stats
     */
    public RetentionLeaseStats getRetentionLeaseStats() {
        return retentionLeaseStats;
    }
    public String getDataPath() {
        return dataPath;