You can assign the “category” taxonomy to post type that you want, but it’s still 1 taxonomy and thus shared between any that it is registered to, it’s not isolated per
That’s correct. That’s why the plugin I mentioned is handy: you can choose to make posts and/or pages appear under the category I assign to pages, thus having the division between posts and pages I needed.
As I said, that solved the problem I had just with CPT, that is: calling the category showed no posts / pages / other content.