If Google Authenticator codes aren't restored, then I'm guessing you're restoring to another device. Google Authenticator presumably uses the keychain, and for

If Google Authenticator codes aren't restored, then I'm guessing you're restoring to another device. Google Authenticator presumably uses the keychain, and for keychain items, unless the item has opted-in to iCloud syncing, the keychain item can only be restored to the device that created it. Which is to say, there's two distinct chunks of keychain data. There's the local-only items, and the iCloud-synced items. The local-only items use a secret known to the device when encrypting, so they cannot be decrypted anywhere else. iCloud-synced items are of course encrypted in a manner that allows them to be decrypted on another device (otherwise syncing wouldn't work). tl;dr: If you restore your encrypted backup to the phone that created it, you get your full keychain back. If you restore it to another phone, you only get keychain items that opted in to iCloud syncing.