Dear Mrs Rapp,
I don't know who reported this to you or in which app or website they found that. But I can say that all the ways on Burg Satzvey were already tagged with an access restriction. It can be possible that the website or app that they used does not use this information that is stored in the OpenStreetMap.org database but it was definitely there. So it could be an issue with the app or the website, if it does not use this data. But I have to admit that the tagging here in our database also wasn't the best possible. I changed it to a more fitting one. But remember, it is still not fully tagged as private, because you have the Weihnachtsmarkt or Mittelaltermarkt, where the area is opened to the public and people can use the ways. We have a tag for that which I used instead now.