[Backport 2.x] Change the output error message back to use OpenSearchException in the cause chain

[opensearch-trigger-bot]

Backport d479853 from #5081.

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: UNSTABLE ❌
• URL: https://build.ci.opensearch.org/job/gradle-check/6390/
• CommitID: 31905d1
  Please examine the workflow log, locate, and copy-paste the failure below, then iterate to green.
  Is the failure a flaky test unrelated to your change?

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: FAILURE ❌
• URL: https://build.ci.opensearch.org/job/gradle-check/6400/
• CommitID: 31905d1
  Please examine the workflow log, locate, and copy-paste the failure 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/6638/
• CommitID: 31905d1

[codecov-commenter]

Codecov Report

Merging #5084 (31905d1) into 2.x (771d7f1) will decrease coverage by 0.10%.
The diff coverage is 100.00%.

@@             Coverage Diff              @@
##                2.x    #5084      +/-   ##
============================================
- Coverage     70.77%   70.67%   -0.11%     
+ Complexity    58398    58314      -84     
============================================
  Files          4699     4699              
  Lines        279034   279034              
  Branches      40736    40737       +1     
============================================
- Hits         197497   197211     -286     
- Misses        65105    65411     +306     
+ Partials      16432    16412      -20     

Impacted Files	Coverage Δ
.../main/java/org/opensearch/OpenSearchException.java	92.04% <100.00%> (-0.21%)	⬇️
...adonly/AddIndexBlockClusterStateUpdateRequest.java	0.00% <0.00%> (-75.00%)	⬇️
...readonly/TransportVerifyShardIndexBlockAction.java	9.75% <0.00%> (-73.18%)	⬇️
...ava/org/opensearch/action/NoSuchNodeException.java	0.00% <0.00%> (-50.00%)	⬇️
.../admin/cluster/reroute/ClusterRerouteResponse.java	60.00% <0.00%> (-40.00%)	⬇️
...indices/readonly/TransportAddIndexBlockAction.java	20.68% <0.00%> (-37.94%)	⬇️
...luster/routing/allocation/RoutingExplanations.java	62.06% <0.00%> (-37.94%)	⬇️
...cluster/coordination/PublishClusterStateStats.java	33.33% <0.00%> (-37.51%)	⬇️
...n/decider/SnapshotInProgressAllocationDecider.java	34.78% <0.00%> (-34.79%)	⬇️
...ion/admin/cluster/node/info/PluginsAndModules.java	53.12% <0.00%> (-34.38%)	⬇️
... and 451 more

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