Categories widget reports categories without posts when they have custom posts

[pkwooster]

This problem may be related to #14084, but this report is specific to the behaviour of the Categories Widget.

• Create a custom post type eg. "Products"
• Create a category eg. "Photographs"
• Add some posts of type Products, assign them to category Photographs
• go to the blog page and the Categories widget lists Photographs as a category
• click on Photographs
• the "Nothing Found" post is shown.

There are no normal posts of category Photographs, but the widget lists a category that returns nothing. I would have expected the widget not to list a category that has no normal posts.

[dd32]

Also similarily related to #14084 is #14073 which describes this same problem.

tl;dr: Term post counts are global to Post Types and Post Statuses, this is a limitation of the existing storage mechanism, and there isn't much we can do until we add Term Meta #10142