You’re dealing with taxonomies for the most part. “category” and “tag” that WordPress creates out of box, are both taxonomies. They allow you to create your own taxonomies as well. “categories” and “tags” and any custom taxonomy you create all get terms created. A category of “comedy” is a term, a tag of “watched” is a term, in an example post type of “movies”
Terms in taxonomies get archives, where you can visit URLs that show all posts that have the given term. Say you wanted to see all of the comedies that have been watched. You visit mysite.com/category/comedy/ and it shows all of those posts.
Your active theme can have template files specific for these archives, that you can customize any which way you want.
Your bullet point here:
Display BRAND posts from category X on a page titled category X and BRAND posts from category Y on a page titled category Y
More or less described category X and Y’s archives to the letter, pun intended ??
We still have zero control over this item though:
select how to display the content on those pages – number of columns, post order, hover effect…
Because we don’t influence the themes at all with CPTUI.
Then with:
automatically update those category pages as soon as new BRAND posts are added to the respective categories x or Y
That’s how the archives work out of box. Once a new brand post is added with the appropriate category, they’ll just automatically show up in the archive.