The screenshot looks like a menu, here is how I would do it:

Custom Taxonomy

Add a new taxonomy for your products e.g. ‘Product Type’ ‘Product Section’ or ‘Product Category’. It’s tempting to assign post categories to that post type but it comes with other issues if you do that, so don’t.

You’ll want to use register_taxonomy, and to list the terms, you’ll want to look at functions such as get_terms to retrieve the top level terms that dont have parents, then repeat for the next level down