You are quite correct - in that the Apple Store App now requires iOS13 or later.
A first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.1. With iOS 12.5.1 installed, you must have one of these three models.
Apple ended major update support for these models of iPad in September 2019 - although they since continue to received “point” security updates. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.
Some App developers, including Apple, have dropped support for some Apps with iOS versions preceding iOS 13.x - most often for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions).
Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS14.
Returning explicitly to the Apple Store App, if the pre-iOS13 version of the App Store has been deleted from your iPad, you’ll not be able to reinstall the App. However, functions and services provided by the App can be still be directly accessed from the Apple Website.
I hope this information and clarification proves to helpful - and similarly clarifies some of the limitations of your existing iPad.
