Set application logger for k8s klog as well

[der-eismann]

Issue #, if available:
Fixes #1150

Description of changes:

As mentioned in #1150 the logs coming from the k8s library directly were in a different logging format. With this change it should be the same (see https://github.com/kubernetes/client-go/issues/18), I now got this:

{"level":"info","v":0,"time":"2025-03-25T11:03:13Z","message":"Waited for 1.192318364s due to client-side throttling, not priority and fairness, request: GET:https://10.10.0.1:443/api/v1/namespaces/default/pods/my-pod-5d447b475f-wrz7l"}

How you tested your changes:
Environment (Linux / Windows): Linux
Kubernetes Version: 1.32

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.