[Remote Routing Table] Refactor Remote routing table interfaces

[himshikha]

Is your feature request related to a problem? Please describe

• Refactor Remote routing table interfaces to use remote interfaces from PR [Remote Cluster State] Remote state interfaces  #13785
• Remove deadCode - https://github.com/opensearch-project/OpenSearch/blob/main/server/src/main/java/org/opensearch/index/remote/RemoteStorePathStrategy.java#L110
• basePath to be constructed directly in RemoteRutingTableService since its moved to utils as part of refactoring https://github.com/opensearch-project/OpenSearch/blob/main/server/src/main/java/org/opensearch/gateway/remote/RemoteClusterStateService.java#L560

Related component

ShardManagement:Routing

[peternied]

[Triage - attendees 1 2 3 4 5]
@rwali-aws Was this missed during the last triage meeting?