@manics: Thank for your help. You’re right, it could be a better idea to run the service in a another pod. The only real downside I see, is that the deployment of the service would not be within the standard helm deployment, but that 's manageable. I will try that.
Nevertheless, it should be possible to run the service within the hub pod. I just stumbled upon this thread: Running dash app as a Hub Service in EKS. In that case the service is indeed running as a hub-managed service within the same pod. So maybe it’s rather a configuration problem, or a bug in the ‘jhub-apps’ service itself.
If I’m not succeeding with ‘jhub-apps’ in a another pod, I will try to deploy one of the simpler services, like this one jupyterhub/examples/service-whoami-flask at main · jupyterhub/jupyterhub · GitHub as a hub-managed service.