The Dynamic checkout button is generated from Shopify base on the configuration on the Checkout Payment in Shopify Admin. So, I'm afraid that we can't touch more on this button to edit style.
In the case you want to have the 'Buy Now' button which we can click on then, it will go to the Checkout page directly, you could consider enabling the 'Checkout' option in the (P) Cart element. This article will help you understand more my idea.
Please try it and let us know how your thoughts.
Thank you so much
Please provide website url and if your store is password protected then also provide password So I will check and provide a solution here.
To customize on checkout page. You need enable Checkout plus, you can contact Shopify support and ask them to enable it for you.
Hope this helps!