I believe it's not possible. UI can be copied but all the functionalities of the product page are implemented using the JS (which is in the minified version like themes/new-theme/public/product_edit.bundle.js) so understanding and editing the JS file is impossible.
So it is better to create your UI and JS.
If you are referring to the product listing page, then use the helper list. You can create custom filters as well using the helperlist.