The first generation iPad Air is obsolete - and, as you observe, is not capable of update to iPadOS 13 or later.
Regrettably, finding mainstream Apps that remain available/compatible with iOS 12 and earlier is increasingly difficult. Many App Developers only support the current and perhaps one or two prior major versions of iOS/iPadOS.
Your current iPad is increasingly limited in both capability and utility. You would be best advised to consider replacing your iPad with a much newer model - as this will provide significantly better choice of available Apps.
For information, here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:
32-bit devices (obsolete)
iPad1 - iOS 5.1.1
iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi+Cellular)
iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi+Cellular)
64-bit devices
iPad Air1*, iPad mini2 and iPad mini3* - iOS 12.5.7
iPad Air2, iPad mini4 - iPadOS 15.8.3
iPad5, iPad Pro (9.7"/12.9" 1st generation)* - iPadOS 16.7.10
iPad6, iPad Pro (10.5"/12.9" 2nd generation) - iPadOS 17.7.5
(*) obsolete
Newer models are all able to be updated to the current version - iPadOS 18.3.1
- iPad Pro 13" (M4)
- iPad Pro 12.9" (3rd generation and later)
- iPad Pro 11" (1st generation and later + M4)
- iPad Air (3rd generation and later + M2)
- iPad (7th generation and later)
- iPad mini (5th generation and later + A17 Pro)