Can I update my iPad Air 2 to iOS 16?

The Air2 is capable of update to iPadOS 15.8.x; the Air2 fundamentally does not support iPadOS16 or later.

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 17.7.2

(*) obsolete

Newer models are all able to be updated to the current version - iPadOS 18.1.1 (17.7.2 optional)

• 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)

If you want or need to use Apps that require a more recent version of iPadOS than you iPad is capable, you have no alternative other than to replace your iPad with a much newer or current model iPad.

no

Current: iPadOS 15.8.3, released July 29, 2024[1]

is end of the line for that model

iPad Air 2 - Wikipedia