[BUG] Improve the integration test for Index management

[bbarani]

Describe the bug
The current integration test for Index management is very flaky and need to be fixed to improve the quality of the artifact

To Reproduce
Refer to this issue for more details

Expected behavior
The test results are reproducible and consistent on every runs

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• Version [e.g. 22]

Additional context
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[downsrob]

All of the known flaky tests for index management were fixed on main with this PR #211. Since that was merged on December 3rd there haven't been any flaky failures on the github CI. This flakiness is not fixed in 1.2 or any of the patch versions, which is why so much flakiness was experienced throughout the many 1.2 patches, but it should be resolved in 1.3 and onward.