Vegan products as such do not exist as such, carrots are not by nature anything other than a carrot and a horsefly a horsefly. neither can be described as a vegan product.
The term produce implies the creation of something to be used and it the concept of use that defines whether something is vegan or not.
A cat is a cat, but a pet is not vegan as it is a use of an animal, no matter how benign the user may consider their act.
Vegan produce, such as that are sold in the most common consumer items is a never ending list of foods and clothing primarily. The simple evidence is whether it contains any notable animal products, milk, wool etc. It is far more difficult to access, paper, cars, computers etc. and so the degree or use is always the question and hence we revert to the concept that vegan really applies to the act not the product. To label a carrot as vegan is the beginning of nonsense fruit and vegetables are not vegan.
And of course the method of producing fruit and vegetable may well include the use of animals both in labour and their by-products.