Wrong term count for private posts

[xknown]

The term manager page (wp-admin/edit-tags.php) shows wrong counts when the terms contain private posts.

Steps to reproduce:

• Create a private post and assign it to a category or a tag.
• Visit the wp-admin/edit-tags.php

The term count does not change. However, when you click on the posts column, the edit posts screen will correctly show the private post.

Term counts are not calculated on the fly. Rather, only published posts count here, and they are stored with the term. See _update_post_term_count(). Known limitation, unfortunately.