Automatic merge from submit-queue. If you want to cherry-pick this change to another branch, please follow the instructions <a href="https://github.com/kubernetes/community/blob/master/contributors/devel/cherry-picks.md">here</a>.
[e2e service] Move apiserver restart validation logic into util
**What this PR does / why we need it**:
Follow up of #60906, on GKE apiserver pod is invisible on k8s, hence test is failing.
This PR bakes the restart validation logic into the util function instead so it could be env-awared.
**Which issue(s) this PR fixes** *(optional, in `fixes #<issue number>(, fixes #<issue_number>, ...)` format, will close the issue(s) when PR gets merged)*:
Fixes#60761
**Special notes for your reviewer**:
Sorry for the noise.
/assign @rramkumar1 @bowei
cc @krzyzacy
**Release note**:
```release-note
NONE
```
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