My iPad Air says I’m up to date with 12.1.5. Why can’t I get iOS 14?

Your iPad Air model cannot upgrade/update beyond any version of iOS 12, currently at iOS 12.5.1

The 2013 iPad Air 1, iPad Mini 2 and 2014 iPad Mini 3 have overall internal hardware that is too old, too underpowered and incapable of running all of the new, advanced and internal hardware resource intensive features of iPadOS.

Sorry.

There is one last thing you can try/attempt, if you need an older version of an app.

If you own much newer iOS device that can run iOS/iPadOS 13 and later, you can install the most recent app/s onto that more recent iOS device.

Then go back to your older iPad, open the iOS App Store, go to the Purchases section of the store app, search for the app/s you wish to try and download to that older iPad and see if an older version of the app is allowed to be downloaded/installed to that older iPad.

These newer iOS/iPadOS devices must use your same Apple ID user account and password.

Failing that OR IF NO joy, then there is nothing more to be done.

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a new iPad model OR a much “newer” , used iPad model capable of running the latest iPadOS versions. There are plenty of newer, older iPad models that can run the latest, current versions of iPadOS.

Sorry & Best of Luck to You!