You're looking at that screen in Google Drive I assume? If so, the only way I know of to restore that data is after a factory reset.
You could sign out of your Google account, and then sign back in. That would give you the option to restore apps, but only apps I believe. In that backup are also wifi passwords, phone settings, home screen layouts, etc, that I have only been able to restore after a factory reset. When you login to your account, you are given a few options to restore, like Bluetooth to an old phone or connect a cable to an old phone. Another option is to use that Google backup to restore from.