How to modify add to cart form in detail
I realise this answer may be a little late, but for those that end up here looking for a way to display the product variation fields (price, add to cart buttons, etc) separately, you can do it through the commerce-product.html.twig template using something like this:

&lt;article{{ attributes }}&gt;
  {{ product.title }}
  {{ product.body }}
  {{ product.variation_price }}
  {{ product.variations }} //show add to cart button
&lt;/article&gt;