Delivery method customisation using Shopify functions

I need to add delivery method to product page, so that customers can check which method is available and select available method in product page, and selected method should only display in checkout page. Tried delivery customisation function, but as per documentation it suggested me to use checkout UI for any modifications in delivery methods, so was bit confused what to do next. Any help or suggestions where to find similar one, or is this kind of function posible to create using functions?

Functions are typically just for the checkout pages - so you might be better checking out the Storefront API (or Liquid) for this.