[3.5] Implement etcd process go fail client timeout

[ivanvc]

This PR backports EtcdProcess's GoFailClientTimeout, as requested in #17425.

Required to backport #16822.

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

[k8s-ci-robot]

Hi @ivanvc. Thanks for your PR.

I'm waiting for a etcd-io member to verify that this patch is reasonable to test. If it is, they should reply with /ok-to-test on its own line. Until that is done, I will not automatically test new commits in this PR, but the usual testing commands by org members will still work. Regular contributors should join the org to skip this step.

Once the patch is verified, the new status will be reflected by the ok-to-test label.

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[jmhbnz]

/ok-to-test

[ahrtr]

lgtm

Thanks