Ah, someone who cares about privacy, nice! I think I have only good news for you:

Direct Contributions

First off, understand that with this app, you make actual and direct contributions to the OpenStreetMap.
Anything you contribute in this app is directly added to the map, there is no third party in-between the app and OSM infrastructure, like it is the case with wheelmap.org or Kort.

Editing the OpenStreetMap anonymously is not possible, so any changes you make are made with your OSM user account. This means, that the date, content and implicitly the location of your changes are visible publicly on the openstreetmap website and are attributable to your account.

Location

The app does not share your GPS location with anyone. It is used to automatically scan for quests around your area and to focus (and thus download) the map around your location.

Data Usage

As mentioned, the app directly communicates with OSM infrastructure. That is, with the Overpass API for downloading quests (which is anonymous) and with the OSM API for uploading changes.
However, before uploading your changes, the app checks with a simple text file on my server whether it has been banned from uploading any changes. This is a precautionary measure to be able to keep versions of the app that turn out to have critical bugs from possibly corrupting OSM data.

To display the map, vector tiles are retrieved from map-data.de. The service logs tile requests for anonymous statistics and for detecting issues but deletes the logs after a few days.

For some quests, some additional data from third parties is downloaded. In particular, the oneway quest queries an API, also hosted on westnordost.de, about likely candidates for oneways.

Photos you attach to a note are uploaded to my server and deleted some days after that note has been resolved. Their meta-data is stripped before upload.