Custom Taxonomies in body class with parent slug

I have tried many answers here on stackoverflow but couldnt find a solution to my problem. I have created a custom post type called ph_products and custom taxonomies with the name ph_category.

Then I created some categories for that custom post type like this:

blue-products
    blue-sub-products
green-products
red-products

I need to have body classes as following:

When on the ph_products-archive page there should be a class with that slug in the body

When on one of the parent categories the respective slug should be in the body class

And when I am on one of the sub category archive pages I need to also have the parent category class

For example I am at the blue-sub-products archive page I want to have blue-products, ph_products-archive, blue-sub-products in the body class

Of course I need all of these classes in the respective single views of the products as well.

I use this piece of code to add the desired classes:

(thanks to https://alexanderdejong.com/wordpress/add-custom-taxonomies-body-class)

function atp_custom_taxonomy_body_class($classes, $class, $ID) {

    $taxonomies_args = array(
        'public' = true,
        '_builtin' = false,
    );

    $taxonomies = get_taxonomies( $taxonomies_args, 'names', 'and' );
    foreach ($taxonomies as $taxonomy) {

        $terms = get_the_terms( (int) $ID, $taxonomy );

        if ( ! empty( $terms ) ) {
            foreach ( (array) $terms as $order = $term ) {
                if ( ! in_array( $term-slug, $classes ) ) {
                    $classes[] = $term-slug;
                }
            }
        }
    }

    return $classes;
}
add_filter( 'body_class', 'atp_custom_taxonomy_body_class', 10, 3 );

But this kinda adds the classes pretty weird for example when I am on the ph_products-archive page I also get the category slugs of the last item posted there so if the last item is in the categories blue-products, blue-sub-products I get these two slugs as classes as well although I am not at these category pages

Or when I am at the blue-products-archive page I also get the blue-sub-products category slug in the body class.

How can I only get the classes desired as described above?