[3.4] chore(e2e): backport TestNoErrorLogsDuringNormalOperations test

[ghouscht]

Backport of #18806 to release-3.4 branch.

Please read https://github.com/etcd-io/etcd/blob/main/CONTRIBUTING.md#contribution-flow.

[k8s-ci-robot]

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[ivanvc]

/retitle [3.4] chore(e2e): backport TestNoErrorLogsDuringNormalOperations test
/ok-to-test

[k8s-ci-robot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: ahrtr, fuweid, ghouscht, serathius

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