[Backport 2.17] Initialize RemoteRoutingTableService when we have RoutingTableRepos

[opensearch-trigger-bot]

Backport e087272 from #15645.

[github-actions]

❌ Gradle check result for f01e41f: null

Please examine the workflow log, locate, and copy-paste the failure(s) below, then iterate to green. Is the failure a flaky test unrelated to your change?

[github-actions]

❕ Gradle check result for f01e41f: 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

All modified and coverable lines are covered by tests ✅

Project coverage is 71.73%. Comparing base (3f95aa2) to head (f01e41f).
Report is 2 commits behind head on 2.17.

Additional details and impacted files

@@             Coverage Diff              @@
##               2.17   #15654      +/-   ##
============================================
+ Coverage     71.62%   71.73%   +0.11%     
- Complexity    63996    64081      +85     
============================================
  Files          5248     5248              
  Lines        299513   299513              
  Branches      43609    43609              
============================================
+ Hits         214524   214857     +333     
+ Misses        67022    66725     -297     
+ Partials      17967    17931      -36     

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