Once you have restored within the new look app any classic recipe pack purchases will show up under a new recipe item "classic recipe packs". The recipes will also always be available via search and as part of Jamie's collections.
To restore open the app and navigate to the More Menu > Settings > Restore Purchases. When prompted please take care to enter the same Apple ID that you used to make the original purchase. You will need a connection to the internet for this to work, ideally WiFi although it will work via cellular data network. Restore may take a couple of minutes to complete, but it can take longer depending on your connection.
If you are having problems restoring a subscription please do bear in mind that once your subscription ended, you will no longer be able to access all of the recipes, only the free taster pack, plus any packs you purchased before the app moved to subscription.
Apple keep a record of every purchase made against your Apple ID and handle much of the restore process.
If you are still having problems Restoring please try uninstalling the app, restarting your device, and then reinstalling the app again from the App Store, before attempting to reinstall again.