Products in Storyblok Commerce can have multiple categories assigned. The assignment of a product defines the visibility of a specific product in that category.
You want that the product T-shirt is visible on the UK store and in the category Men and T-Shirts. Therefore you need to create the category with the slug en-uk for UK-Store, a category with the slug men and a category with the slug t-shirts.
When using the CSV import the assignment needs to be defined by putting in the slugs of the categories you want to assign: