How granular can the app developer set the permissions to avoid turning the user away at the "Permissions to Photos, Media and Other files"?
PMOF means android.permission.[READ|WRITE]_EXTERNAL_STORAGE, which, once granted, allows app to read whole /sdcard. See this answer for details how this happens at back end. Now the app can read / write / inspect /delete / rename / modify / upload / encrypt whatever you have in shared public storage including photos, videos, documents, contacts, messages, backups and so on.

Unfortunately Android offers no more granular control over this filesystem level access. However Storage Access Framework (SAF) can be used to not let app access whole /sdcard filesystem, but only a specific file or directory (included subdirectories).

Android Q is introducing a more fine-grained control with Scoped Storage.