does my new IPad air 3 support facial recognition?

Another short answer - facial recognition is only supported by devices that utilise FaceID instead of TouchID.

TouchID is built into the Home Button of iPad and iPhone - whereas iPads with FaceID do not have a Home Button. FaceID technology is therefore only available on 2018 and 2020 models of iPad Pro.

Short answer. No.

Hello,

Face ID requires an iPad model with a True Depth Camera:

iPad Pro 11-inch (1st generation)

iPad Pro 11-inch (2nd generation)

iPad Pro 12.9-inch (3rd generation)

iPad Pro 12.9-inch (4th generation)