As described, the App that you have been using has been withdrawn from the App Store by the Developer. While the existing downloaded App has continued to work with iPadOS15, your description indicates that the App is fundamentally incompatible with iPadOS16. Such issues can occur when older system-libraries, upon which Apps often rely for core functionality, are deprecated and removed from the Operating System.
As an updated version of the App, compatible with iPadOS16 is evidently not available, you’ll not be able to access data (recipes) that you have previously stored within the [now] non functioning App.
Your only way forward is to seek assistance from the App Developer - if you are able to do so:
How to contact an app developer - Apple Support
Unless an updated version of the existing App is released, you may be unable to recover any associated data.