The state of Niedersachsen has a dedicated website for showing school locations. The html file actually contains all locations of all schools along with (unfortunately nothing more than) their names.
It can be found at https://www.nls.niedersachsen.de/Schulkarten/Schulen_in_Niedersachsen_2024.html
I think we could try to run our existing scrapers for Niedersachsen and to also load the schools with their locations from the new endpoint. We could then string-match the names to their locations. A bit hacky but the closest to official geo data that I was able to find for the state.