'privileged' problem in the supervisor


I am not sure if this is the right category, because my installation is not a fresh one but running for quite a long time now.

Home assistant started to mark my installation as faulty, because the supervisor (running in docker) is missing privileged access.
I was running the convenience installation script several times now, but the problem is still existing. I read several threads about this ‘privileged’ problem, but none of them came up with a solution that worked for me.

Does anyone have an idea, which settings might be wrong in my environment, or which property in docker or the HA config could be wrong or missing? I would like to automatically update to the latest version, but that does not work if the supervisor is faulty…