[Backport 2.x] Optimize remote state stale file deletion (#13995)

[shiv0408]

(cherry picked from commit 3de5d3c)

Description

Backport 3de5d3c from #13995

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 4490b3f: 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.

[github-actions]

❌ Gradle check result for 41f493f: 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?

[shiv0408]

org.opensearch.remotemigration.RemoteMigrationIndexMetadataUpdateIT.testRemoteIndexPathFileExistsAfterMigration - #13939
org.opensearch.remotemigration.RemoteReplicaRecoveryIT.testReplicaRecovery - #13473

[github-actions]

❌ Gradle check result for 01f1499: 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 7af2741: 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 9eea466: 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 b1aaddd:

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 48a0eb0: SUCCESS

[codecov]

Codecov Report

Attention: Patch coverage is 77.95699% with 41 lines in your changes missing coverage. Please review.

Project coverage is 71.32%. Comparing base (0dd892c) to head (48a0eb0).
Report is 317 commits behind head on 2.x.

Files	Patch %	Lines
...teway/remote/RemoteClusterStateCleanupManager.java	79.31%	29 Missing and 7 partials ⚠️
...arch/gateway/remote/RemoteClusterStateService.java	55.55%	3 Missing and 1 partial ⚠️
server/src/main/java/org/opensearch/node/Node.java	66.66%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##                2.x   #14025      +/-   ##
============================================
+ Coverage     71.28%   71.32%   +0.04%     
- Complexity    60145    61491    +1346     
============================================
  Files          4957     5050      +93     
  Lines        282799   289150    +6351     
  Branches      41409    42221     +812     
============================================
+ Hits         201591   206245    +4654     
- Misses        64189    65593    +1404     
- Partials      17019    17312     +293     

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[shiv0408]

❌ Gradle check result for 9eea466: FAILURE

org.opensearch.repositories.azure.AzureBlobStoreRepositoryTests.testSnapshotAndRestore - #11493
org.opensearch.repositories.azure.AzureBlobStoreRepositoryTests.classMethod
org.opensearch.action.admin.indices.create.RemoteSplitIndexIT.testCreateSplitIndex - #5409
org.opensearch.remotemigration.RemoteReplicaRecoveryIT.testReplicaRecovery - #13473