I tested it here and in another community and found that while subcategories show, any private top-level categories do not exhibit this issue.
For example, if I link both the Support category (a public category) and the Discourse Experts category (a private category), no embed in the Experts category appears (which may be by design, but I found it interesting). So, if I had access to a private top-level category but not all of the subcategories, I would be unable to see the subcategories when linking the top-level category in the composer.
