Automatic merge from submit-queue (batch tested with PRs 64140, 64898, 65022, 65037, 65027). 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>.

Use actual etcd client for /healthz/etcd checks

* avoids redialing etcd on every health check (which makes slow DNS a false-positive healthz failure)
* ensures etcd TLS setup is correct (errors verifying the etcd API or sending client credentials manifest as healthz failures)
* ensures the etcd cluster is actually responsive

fixes #64909

```release-note
Etcd health checks by the apiserver now ensure the apiserver can connect to and exercise the etcd API
```