Device backups are an entirely different system, not handled by the Drive app, that produces opaque backup archives which aren't accessible via the Drive UI. Nextcloud isn't complaining about lack of access to this system, but to the file-level APIs (e.g. java.io/java.nio classes) that allow for full backups of whatever the app has system-level permission to read.
This permission still doesn’t have the same access as the backup utility, but that is another issue really. If they aren’t willing to open that up then they need to allow for pluggable 3rd party storage backends.
Define "storage backend". You can implement a FileProvider to plug into the Storage Access Framework as a provider, so other apps can browse and request permissions for all of your app's files. You can use the Storage Access Framework as a consumer and ask the user for permissions to read any directory on external storage that is not Downloads/ or Android/{data,obb}, and any files exposed by other apps. Google's own apps use these APIs and do not declare MANAGE_EXTERNAL_STORAGE.
