Introduce the new Primary Category picker to the Classic Editor

[jcomack]

Currently the Primary Category picker in the Classic editor is heavily reliant on the HTML that is returned by WordPress when adding a new category. Because of this, access to important data regarding the new category, is non-existent. The new Category Picker does seem to have access to this data.

By gaining this access, we'd be able to fix an issue where the permalink structure for the Snippet Preview isn't updated accordingly based on newly added categories.