For very large companies that do business in many countries regulators have various concerns (power of the company relative to the country, jurisdiction shopping via choice of headquarters location, etc) that don't apply for the typical case of a German company with a German audience.
On filing complaints and being informed that they were forwarded to the local authority that has jurisdiction.
https://gdpr.eu/article-55-supervisory-authority-competence/ also states Each supervisory authority shall be competent for the performance of the tasks assigned to and the exercise of the powers conferred on it in accordance with this Regulation on the territory of its own Member State, and article 56 adds to that.
