In principle, no data is sent to the authority. Also, your processing directory is not automatically transferred to the authority.
The supervisory authority only requires that you document the processing operations of personal data and that you can provide this documentation to the authority upon request. The authority does not learn any specific data (such as name or e-mail address).
Only if there is a specific occasion, the authority will ask for concrete data, e.g. if someone complains to the authority, the authority will ask for the data of this person in order to verify the complaint.