Pods serving webhooks are missing readiness probes

[timebertt]

How to categorize this issue?

/area robustness
/kind enhancement
/platform azure

What would you like to be added:

Both the extension pods running in the seed and the validator pods running in the garden are missing readinessProbes.
We should add them to minimize webhook failures because of request being sent to unready pods.

[dkistner]

I would recommend to vendor and use the default health manager from g/g here: https://github.com/gardener/gardener/blob/master/pkg/healthz/default.go

[timebertt]

healthz.defaultHealthz doesn't implement the controller-runtime interface healthz.Checker.
I would go for the upstream healthz.Ping just like in gardener-admission-controller: https://github.com/gardener/gardener/blob/e77a0606aee264a703d2bc2727104c2db0d60951/cmd/gardener-admission-controller/app/gardener_admission_controller.go#L167-L169