As many other users, I have the same problem that the Apple Pay button is not shown in my website's check out too. No people can use Apple Pay to check out in my website now. I enable Shop Payment and choose Apple Pay in the setting. Even I remove Google Pay, the Apple Pay button still cannot show. I tried in iPhone 13 Pro but it shows Google Pay.
Just a few points for clarity when it comes to Apple Pay:
Apple Pay can be displayed on the cart OR the customer information page of the checkout, not both. Apple Pay is not expected to show on the Payment Method stage of checkout. Since accelerated methods of this kind include shipping information, including it further in the checkout process is redundant.
Apple Pay will only work on Shopify's web checkout, meaning native checkouts through Twitter and Facebook will not support Apple Pay.
Apple Pay will also not work with the Buy Button channel.
Please cross-check your store against these requirements.