[Backport 2.x] Unify internal OpenSearch exceptions with returned status code

[opensearch-trigger-bot[bot]]

Backport 4c44f56f3eed5926430acf2c6a12151cbf182162 from #3068.

[codecov[bot]]

Codecov Report

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

Project coverage is 94.48%. Comparing base (34a5fe5) to head (8f1671d). Report is 6 commits behind head on 2.x.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## 2.x #3072 +/- ## ========================================= Coverage 94.48% 94.48% - Complexity 5415 5416 +1 ========================================= Files 528 528 Lines 15436 15436 Branches 1010 1010 ========================================= Hits 14585 14585 Misses 804 804 Partials 47 47 ``` | [Flag](https://app.codecov.io/gh/opensearch-project/sql/pull/3072/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=opensearch-project) | Coverage Δ | | |---|---|---| | [sql-engine](https://app.codecov.io/gh/opensearch-project/sql/pull/3072/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=opensearch-project) | `94.48% <100.00%> (ø)` | | Flags with carried forward coverage won't be shown. [Click here](https://docs.codecov.io/docs/carryforward-flags?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=opensearch-project#carryforward-flags-in-the-pull-request-comment) to find out more.

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[noCharger]

@Swiddis could you double check the CI?

Execution failed for task ':integ-test:integTest'.
> There were failing tests. See the report at: file:///D:/a/sql/sql/integ-test/build/reports/tests/integTest/index.html

[Swiddis]

@noCharger CI is failing because this fixed breakage by #3066 (backport #3084) getting merged with failing tests. The PR depends on that PR being merged to get the tests passing again. I opened #3070 to prevent recurrence.

[Swiddis]

Will merge this for now, fast followup is to merge #3084