Hi Martin! Thanks so much for your congrats :)
About your question, well, if you apply the ingress with a manifest like this https://raw.githubusercontent.com/kubernetes/ingress-nginx/controller-v0.35.0/deploy/static/provider/cloud/deploy.yaml
for a static (or generic) deployment (not AWS, GCP, etc), you can check the health port.
This health port is checked by the load balancer periodically to determine if the service is up or not. If the service is up then it send traffic to it.
If you view the "deploy.yaml" file you can check under the "deployment" kind, the "livenessprobe" section.
You must take note about the path and port and use it in the hetzner LB annotations.
I hope this clarifies your question. If not, don't hesitate to question again.