get_categories() only lists categories, so you shouldn’t be seeing any terms from the custom taxonomy. What you want to use is get_terms() which takes a taxonomy as an argument. As you can read about in this answer, get_terms() is actually used by get_categories(), it just prefills the “taxonomy” argument with “category.”
If you swap in get_terms() and add the name of your custom taxonomy, your code looks like it should work. The only other thing you may be able to change is your if statement checking the category count. If you’re already doing 'hide_empty' => 1 you shouldn’t need that.
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