[Backport 2.x] Fix custom metadata not getting stored for remote store not supporting async write

[opensearch-trigger-bot]

Backport e618b9b from #10812.

[github-actions]

Compatibility status:

Checks if related components are compatible with change 35c6272

Incompatible components

Incompatible components: [https://github.com/opensearch-project/security-analytics.git]

Skipped components

Compatible components

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

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: FAILURE ❌
• URL: https://build.ci.opensearch.org/job/gradle-check/28714/
• CommitID: 35c6272
  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?

[shwetathareja]

Flaky Test - https://build.ci.opensearch.org/job/gradle-check/28714/

org.opensearch.search.aggregations.metrics.CardinalityWithRequestBreakerIT.testRequestBreaker {p0={"search.concurrent_segment_search.enabled":"true"}}
org.opensearch.search.suggest.CompletionSuggestSearchIT.testSkipDuplicates {p0={"search.concurrent_segment_search.enabled":"false"}}
org.opensearch.search.suggest.CompletionSuggestSearchIT.testSkipDuplicates {p0={"search.concurrent_segment_search.enabled":"true"}}

Issue - #10798