With the help of my colleague @tristup, we are able to come with a solution using the custom Looper Provider to solve your issue.
1.) First, I activated your child theme and add this custom filter below in your child theme functions.php
add_filter('cs_looper_custom_subcat', function($result, $args)
$category = get_queried_object();
$cat_args = array(
'hide_empty' => 1,
'taxonomy' => 'product_cat',
$subcats = get_categories($cat_args);
}, 10, 2);
that filter will get all the subcategories of a specific category.
2.) Enable the custom in the Looper Provider and add a hook name subcat it is base on the custom filters we added in your child theme functions.php
3.) Remove all the string conditions you added from the above response so that it will apply to all categories.
4.) Your category page is now showing its sub-categories, see the example below:
Hope that helps.