CI: replace netchecker and manual tests of the clusters with a turn-key solution

What would you like to be added

In our CI we do some basics tests of the cluster after a kubespray runs, to validate we did built it correctly.

We should replace it with dedicated tester of Kubernetes functionality, which are already used by others, such as hydrophone : https://github.com/kubernetes-sigs/hydrophone/ We'll need to select a subset of tests, because we want to keep the runtime relatively low (I'd say max 10 minutes for the testsuite, considering our CI jobs are currently < 15 min each, I think).

This would need roughly here : https://github.com/kubernetes-sigs/kubespray/blob/1c008d79b1b617296b0d5427344192adc7403ace/tests/scripts/testcases_run.sh#L82-L87

(and also probably some stuff in the docker image, we want to download / built hydrophone here, not exactly sure how to do that).

Why is this needed

1. Less maintenance for us
2. More alignment with the wider ecosystem

See https://kubernetes.slack.com/archives/C78F00H99/p1763150495755689 for suggestions and context.

/help