Just gonna drop this here for anyone still trying to solve this:
I have spent quite a bit of time with Authorize.net and Shopify trying to resolve this. Both parties naturally want to point the finger at each other. But I was finally able to distill it down to the fact that Shopify simply doesn't support setting up Apple Pay this way. First, they don't support uploading files to the server in the way Apple requires for Domain Verification. And nobody has any clue what is supposed to happen with the Payment Processing Certificate. Everyone just points to everyone else. But Shopify did finally admit that the only way you can verify your domain is via DNS. Naturally, Apple doesnt offer this option. So it's effectively impossible. Shopify claims they will elevate the case and try to add the feature, but they also shared this forum post with me, which is five years old. So Im not convinced they're going to add the ability to domain verify. Basically, I've learned I've made a mistake switching to Shopify.