[Backport 2.x] Allow RemotePublication configured nodes to join remote cluster in mixed mode

[opensearch-trigger-bot]

Backport 5888867 from #15994.

[github-actions]

❌ Gradle check result for 4f628be: FAILURE

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 4f628be: FAILURE

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 4f628be: 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 71.72%. Comparing base (01ea078) to head (4f628be).
Report is 3 commits behind head on 2.x.

Additional details and impacted files

@@             Coverage Diff              @@
##                2.x   #16090      +/-   ##
============================================
+ Coverage     71.68%   71.72%   +0.03%     
+ Complexity    64768    64715      -53     
============================================
  Files          5278     5278              
  Lines        302647   302652       +5     
  Branches      44028    44029       +1     
============================================
+ Hits         216955   217077     +122     
+ Misses        67592    67408     -184     
- Partials      18100    18167      +67     

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