Android adds permission to store and, above all, read files, internally and, above all, on external SD cards together -> Allow access to photos / media / files.
Android does not distinguish between whether this data is purely internally stored on the app or only for the app / call.
Until some time ago, these permissions were queried centrally in the installation bundled in the Play Store and you had to confirm this.
Since Android 6.0 or with apps designed for it, this has changed:
Since then, these permissions are typically requested at the time of use in order for the app to run, e.g. not directly after the installation.
You can also see the entire permissions of an app before installation in detail, in the Play Store on the detail page of the app just click on "Permissions -> View Details".
The access permissions have not changed, if you already used the Onleihe-App before, you already accepted them.