[8.x](backport #41230) Re-enable TestGroup_Go and fix flaky behavior #41236
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Proposed commit message
This PR re-enables the TestGroup_Go test, which was skipped in #41223. It also includes fixes to mitigate flakiness in the test logger caused by timming issues and ensures proper waiting for success conditions within the tests.
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Related issues
This is an automatic backport of pull request Re-enable TestGroup_Go and fix flaky behavior #41230 done by Mergify.