Displaying the post count of all custom taxonomy terms in a list format

You’ll have to use the get_terms function to build your own list if you want the count in there.

If we read the details of topic_count_text_callback we can see why it may appear to not be working:

topic_count_text_callback

(string) (optional) The function, which, given the count of the posts with that tag, returns a text for the tooltip of the tag link.
Default: default_topic_count_text

this function sets the link’s title attribute text, it doesn’t show the count with the term directly in the text. If you hover over the links you’ll see the text pop-up in a tooltip next to your cursor.