[Backport 2.16][Backport 2.x] Refactor remote-routing-table service inline with remote state interfaces (#14668)

[Arpit-Bandejiya]

backport #14862

Description

[Describe what this change achieves]

Related Issues

Resolves #[Issue number to be closed when this PR is merged]

Check List

• Functionality includes testing.
• API changes companion pull request created, if applicable.
• Public documentation issue/PR created, if applicable.

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[github-actions]

❕ Gradle check result for 3f29951: UNSTABLE

Please review all flaky tests that succeeded after retry and create an issue if one does not already exist to track the flaky failure.

[codecov]

Codecov Report

Attention: Patch coverage is 90.90909% with 8 lines in your changes missing coverage. Please review.

Please upload report for BASE (2.16@69bccb9). Learn more about missing BASE report.

Files	Patch %	Lines
...arch/gateway/remote/RemoteClusterStateService.java	73.33%	2 Missing and 2 partials ⚠️
...y/remote/routingtable/RemoteIndexRoutingTable.java	88.88%	1 Missing and 2 partials ⚠️
...eway/remote/model/RemoteRoutingTableBlobStore.java	95.83%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             2.16   #14886   +/-   ##
=======================================
  Coverage        ?   71.51%           
  Complexity      ?    62556           
=======================================
  Files           ?     5110           
  Lines           ?   293651           
  Branches        ?    42791           
=======================================
  Hits            ?   210012           
  Misses          ?    66060           
  Partials        ?    17579           

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