[Backport 2.x] Fix flaky tests 'testDeleteAllAndListAllPits' and 'testDeleteWhileSearch'

[opensearch-trigger-bot]

Backport 8673fa9 from #10946.

[github-actions]

Compatibility status:

Checks if related components are compatible with change 916f30e

Incompatible components

Incompatible components: [https://github.com/opensearch-project/performance-analyzer.git]

Skipped components

Compatible components

Compatible components: [https://github.com/opensearch-project/security.git, https://github.com/opensearch-project/security-analytics.git, https://github.com/opensearch-project/custom-codecs.git, https://github.com/opensearch-project/geospatial.git, https://github.com/opensearch-project/index-management.git, https://github.com/opensearch-project/notifications.git, https://github.com/opensearch-project/sql.git, https://github.com/opensearch-project/job-scheduler.git, https://github.com/opensearch-project/neural-search.git, https://github.com/opensearch-project/observability.git, https://github.com/opensearch-project/k-nn.git, https://github.com/opensearch-project/cross-cluster-replication.git, https://github.com/opensearch-project/alerting.git, https://github.com/opensearch-project/anomaly-detection.git, https://github.com/opensearch-project/asynchronous-search.git, https://github.com/opensearch-project/performance-analyzer-rca.git, https://github.com/opensearch-project/common-utils.git, https://github.com/opensearch-project/reporting.git, https://github.com/opensearch-project/ml-commons.git]

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: UNSTABLE ❕
• TEST FAILURES:

      1 org.opensearch.backwards.MixedClusterClientYamlTestSuiteIT.test {p0=pit/10_basic/Delete all}

• URL: https://build.ci.opensearch.org/job/gradle-check/29434/
• CommitID: 916f30e
  Please review all flaky tests that succeeded after retry and create an issue if one does not already exist to track the flaky failure.