Hi,
Brands are brands. They are not supposed to be listed in categories listings.
It's like if you were asking me if there is a fix to display HikaShop products in joomla article listings.
They are two different entities and like Joomla article listings are not meant to display HikaShop products, categories listings are not meant to display brands. So there is nothing to "fix" here. The issue is conceptual, not code or settings.
One you could do is actually not use a categories listing page to display that first page.
Instead, you should create a Joomla article with four links, each one linking to its category listing menu item or brands listing menu item and then have that article display on a page instead of that categories listing where you're trying to add the brands listing.
Actually, a much simpler solution would be to create a fake "shop by brands" category, and in the "canonical URL" of that category, enter the link of a brands listing menu item, and then make sure that the "force canonical URLs on listings" setting is activated on your HikaShop configuration. That way, you would have a categories listing like you want with the four elements, and the shop by brands would work like you want.