I've found an article describing, that the private space should not be visible from outside, and so some devices cannot connect to an app installed in the private space.
Installing the snapbridge app in a secondary user profile, the app can connect to the camera. To upload the GPS data to the camera the app actually requires the Google play services. But fortunately the play services doesn't need any permissions.
For a comfortable handling an installation in the private space would be really better.
So I hope there will be a solution for this Bluetooth issue in the private space.