[Backport 2.x] [CheckCompatibility] Prevent interleaving of log output

[opensearch-trigger-bot]

Backport 23fd9a5 from #9280.

[opensearch-trigger-bot]

Compatibility status:

> Task :checkCompatibility
Incompatible components: [https://github.com/opensearch-project/security.git, https://github.com/opensearch-project/alerting.git, https://github.com/opensearch-project/anomaly-detection.git, https://github.com/opensearch-project/sql.git, https://github.com/opensearch-project/index-management.git, https://github.com/opensearch-project/common-utils.git, https://github.com/opensearch-project/observability.git, https://github.com/opensearch-project/reporting.git, https://github.com/opensearch-project/cross-cluster-replication.git, https://github.com/opensearch-project/geospatial.git, https://github.com/opensearch-project/ml-commons.git, https://github.com/opensearch-project/k-nn.git, https://github.com/opensearch-project/notifications.git, https://github.com/opensearch-project/neural-search.git, https://github.com/opensearch-project/performance-analyzer.git]
Components skipped due to git failures: [https://github.com/opensearch-project/opensearch-oci-object-storage.git]
Compatible components: [https://github.com/opensearch-project/asynchronous-search.git, https://github.com/opensearch-project/job-scheduler.git, https://github.com/opensearch-project/security-analytics.git, https://github.com/opensearch-project/performance-analyzer-rca.git]

BUILD SUCCESSFUL in 20m 54s

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: FAILURE ❌
• URL: https://build.ci.opensearch.org/job/gradle-check/22785/
• CommitID: ee2f0a3
  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 (Jenkins) Run Completed with:

• RESULT: SUCCESS ✅
• URL: https://build.ci.opensearch.org/job/gradle-check/22818/
• CommitID: ee2f0a3

[codecov]

Codecov Report

Merging #9357 (ee2f0a3) into 2.x (907347a) will decrease coverage by 0.02%.
Report is 6 commits behind head on 2.x.
The diff coverage is 14.28%.

@@             Coverage Diff              @@
##                2.x    #9357      +/-   ##
============================================
- Coverage     70.78%   70.77%   -0.02%     
- Complexity    57499    57503       +4     
============================================
  Files          4761     4761              
  Lines        271850   271849       -1     
  Branches      40088    40087       -1     
============================================
- Hits         192438   192393      -45     
- Misses        62969    62971       +2     
- Partials      16443    16485      +42     

Files Changed	Coverage Δ
...rg/opensearch/gradle/CheckCompatibilityTask.groovy	0.00% <0.00%> (ø)
...in/java/org/opensearch/plugin/noop/NoopPlugin.java	0.00% <ø> (ø)
...ugin/noop/action/bulk/TransportNoopBulkAction.java	0.00% <ø> (ø)
.../noop/action/search/TransportNoopSearchAction.java	0.00% <ø> (ø)
...main/java/org/opensearch/client/ClusterClient.java	8.57% <ø> (ø)
...main/java/org/opensearch/client/IndicesClient.java	1.77% <ø> (ø)
.../main/java/org/opensearch/client/IngestClient.java	15.78% <ø> (ø)
.../java/org/opensearch/client/RequestConverters.java	85.21% <ø> (+0.33%)	⬆️
...ava/org/opensearch/client/RestHighLevelClient.java	41.94% <ø> (ø)
.../java/org/opensearch/client/RethrottleRequest.java	64.28% <ø> (ø)
... and 173 more

... and 460 files with indirect coverage changes