cannot update iPad to 13

The original “first generation” iPad Air cannot be updated to iPadOS 13.x as it lacks the necessary minimum specification to support the newest version.

Update Support for iPad Air ended in September 2019 - the final supported version of iOS being iOS 12.4.7. As such, your description implies that you have already updated to the most recent version of iOS supported by your iPad.

If however you have an iPad Air2, or the current iPad Air3, then you should be able to update to iPadOS 13.4.1. As these models are upgradable to iPadOS 13.x, whose release precedes the final iOS 12.4.7 release, the final iOS 12.x release will not be found on either Air2 or Air3 models.

As such, you clearly have an iPad Air1 - which cannot be updated further. If Apps that you need require iPadOS 13.x, then you have no alternative other than to replace your iPad with a newer model.

Sorry, this is perhaps not the news that you were hoping to hear, but I hope this information is helpful in informing your options.

12.4.7 is the furthest that your iPad is going to allow you to update to. Your device doesn’t meet the requirements for iPadOS 13 so 12.4.7 is the highest and that’s why you keep getting a message that your device is up to date.