[Backport 2.x] Fix stale cluster state custom file deletion

[opensearch-trigger-bot[bot]]

Backport ac443003bad13aeb6373f80439e154dcf25023a2 from #16670.

[github-actions[bot]]

:white_check_mark: Gradle check result for 38eebea363e4a8ba74a04abcb5e8769157758e42: SUCCESS

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 71.88%. Comparing base (407a70d) to head (38eebea). Report is 4 commits behind head on 2.x.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## 2.x #16680 +/- ## ============================================ + Coverage 71.77% 71.88% +0.10% - Complexity 65404 65473 +69 ============================================ Files 5314 5314 Lines 305210 305210 Branches 44473 44473 ============================================ + Hits 219069 219394 +325 + Misses 67908 67594 -314 + Partials 18233 18222 -11 ```

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