If a product belongs to multiple categories in WooCommerce?

Question

Online shopping

Good day!
There is an online cosmetics store. For the convenience of users, the following structure of categories has been created:
- What?
- Mascara
- Powder
- For what?
- For the eyes
- For the face
- From whom?
- Loreal
- Faberlic
For example, let's create a product "Black mascara (3 g)". This product belongs to several categories:
- What? - Mascara
- For what - For the eyes
- From whom? - Loreal
In the canonical link I specify site.ru/chto/tush/tush-chernaya
Now about the problem. When you open a product, the permalink consists of a path under the category "From whom?", and breadcrumbs are made up of a path under the category "For what?".
How can you influence the permalink and breadcrumbs to be based on what is set in the canonical link. Not necessarily automatic, the main thing is that you can change it.
Thanks in advance!

Answer 1

Why not use product attributes, which are already like a taxonomy and provide everything you need. In addition, it is an integral part of WooCommece. And there are permalinks. More details - in the clarifications to the question .