Apple Pay itself does not charge for anything. It is merely a conduit. The charge is made by the merchant, in this case Southwest, and processed by your bank through the Apple Pay platform.
If your bank successfully processed the charge, then Southwest should have received the amount, and only they can refund it.
Follow the steps in the support document you posted from to request a refund from Southwest.
Apple Pay does not hold any money nor can it itself refund anything.
If southwest confirmed the booking did not taker place then they just took your money and did not book a ticket for you.