[Remote Cluster State] Refactor RemoteClusterStateService to small decomposable units for each file write

[shiv0408]

          Can we split this class into small and de-composable units for individual file writes and only retain the coordination logic across files formats here. This class is becoming too unwieldy to manage.

Originally posted by @Bukhtawar in #12190 (comment)

[shiv0408]

RemoteClusterStateService.java is getting to big after granular metadata files upload, we need to refactor that class into smaller classes for each kind of files and only keep the Coordination logic in mentioned file for better code cleanliness and maintainability.

The linked PR has already become too big, adding the refactoring will make that PR very difficult to review. So I have opened this issue to create a separate PR for this refactoring.