How does Nokia automatic backup work on the new Android One devices?
I'm not an expert with this, but here's what I know.
Nokia 6.1 as with all Android One phones, runs stock Android. And the backup/restore options that you see are all part of normal Android and you will see them across nearly all Android smartphones be it Android One or not. So, the backup that is on a Google account can be restored on any other device.

Other OEMs do have a better backup/restore setup and I recommend that you ask her to do a better job at backing up stuff.

The backup setup in Android One is a barebone setup and you'll barely recover anything beyond your list of installed apps and your contacts (inc SMS and call history). Apps which automatically backup to their server or to Google Drive (like WhatsApp) are an exception. For everything else, such as files, documents, photos, videos, music, you need to back them up yourself.

Google Photos is a nice way to keep your photos from the camera all backed up. You can also consider using Microsoft's OneDrive app. For the other items, you need to either sync them to the cloud manually or use a USB cable to copy them to the PC regularly.