Is there a way to have a different featured image set for different post categories?

Assuming you mean different images for posts that are in different categories, then sure. If you’re talking about customised featured images for categories then that’s a bit different, because we’re hooking post meta data here, not term meta data.

For posts, all you need to do is find the primary/first category of the post… because a post/product can be in more than one category.

You could create a little function to get the first category id of a post, like this:

function custom_get_first_category(int $post_id) {
   $category_term = null;

   $category_terms = get_the_category($post_id);
   if (is_array($category_terms) && (count($category_terms) > 0)) {
      $category_term = $category_terms[0]; // <<< This is a WP_Term object
   }

   return $category_term;
}

Then you'll want to comment out the line that checks to see if the post type has is in HW_MISSING_FEATURED_IMAGE_IDS:

   // } elseif (!array_key_exists($post_type, HW_MISSING_FEATURED_IMAGE_IDS)) {

Then you call your new custom_get_first_category() function from the main else{ … } block in custom_default_post_metadata() like this:

} else {
   if (array_key_exists($post_type, HW_MISSING_FEATURED_IMAGE_IDS)) {
      $value = HW_MISSING_FEATURED_IMAGE_IDS[$post_type];
   }

   $post_category = custom_get_first_category($object_id);
   if (!empty($post_category)) {
      switch ($post_category->slug) {
      case 'some_category':
         $value = 123; // Image ID for some_category
         break;

      case 'another_category':
         $value = 456; // Image ID for another_category
         break;

      default:
         // ...
         break;
      }
   }
}

I've not tested this (so watch out for typos) but it should be easy enough to get something working from here.