Allow customers to add arbitrary data to products when adding to cart
For the benefit of anyone who comes looking, the answer is that the fields need to be added to the order item type. Commerce sees each product as a sort of Platonic object and stamps out instances as order items -- think line items. You can add fields to this. Whee. Unfortunately, you can't reference Paragraph entities because, as ridiculous as it seems to me, Paragraph entities only support a single reference.