[Remote State] Evaluate and move remote publication to new thread pool

[soosinha]

Is your feature request related to a problem? Please describe

Currently remote cluster state publication is done using the GENERIC thread pool: https://github.com/opensearch-project/OpenSearch/blob/main/server/src/main/java/org/opensearch/cluster/coordination/PublicationTransportHandler.java#L559

Describe the solution you'd like

Evaluate if we should use a different threadpool. Create a new threadpool and use for remote cluster state publication if needed.

Related component

Cluster Manager

Describe alternatives you've considered

No response

Additional context

No response