Welcome back to the Wefugees Community and thank you for reaching out to us.
I am also not fully sure about your question and tried to make some research. In this brochure (in German though), for instance, they are explaining that only public authorities have to report people without papers. From my understanding, a notary in this case would need to work confidential for his/her clients and functions in a similar role as a lawyer. But I will also link our expert dear @alla_fka here. Maybe she can correct me or share her experience.
In any case, the Standesamt IS a public authority. You should be really careful in dealing with them as they might report your status to the immigration office/police at the end. On the other hand, I did not really understand yet, what kind of paper you want to be issued by the Standesamt. Is it a "Ehefähigkeitszeugnis" to marry abroad? Why would be your documents needed then?
Please feel free to get back to us and to discuss your case further.
All the best,