How are multilingual shops handled with Commerce?
With the separation of products and your catalog, there are many different ways you can build a multilingual shop, but you'll generally need to be using multiple contexts with their own cultureKey and locale system settings to switch out languages.
Product information stored in Commerce is not currently natively translatable, but we've seen people use custom products to fit that needs. If you're not using product stock, you could also duplicate product records across contexts.