Looping Through Categories of a CPT

' publish',

This is your problem, an extra space character.

Note that in future you can catch this by using Query Monitor and by checking if posts were found. Because the post loop is missing an if ( $query->have_posts() ) { ... } else { echo "none found"; } type check, you had no way of knowing where to look for the problem.

Also, you’re listing terms in the filed-under taxonomy:

'taxonomy'  => 'filed-under',

But then you’re passing those terms to the category_name parameter, which is unrelated. So now the terms are being used as if they are terms in the category taxonomy, but they are not.

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