Hook Custom category Menu shortcode to secondary navigation

Hi,

I have a dynamically generated menu which is a shortcode. the menu consist of all categories and sub categories (All levels) of woocommerce products.
What i want is I want to make use of GP secondary navigation. I want to dynamically assign this as secondary navigation without creating any new menu. (probably a function can do)
I want to make use of styling feature of GP secondary navigation to style it.

Please let me know how we can do it.

// Horozontal menu code starts here

function custom_product_category_menu() {
    // Fetch product categories
    $args = array(
        'taxonomy'     => 'product_cat',
        'orderby'      => 'name',
        'show_count'   => 0,
        'pad_counts'   => 0,
        'hierarchical' => 1,
        'title_li'     => '',
        'hide_empty'   => 0
    );

    $all_categories = get_categories($args);

    $menu = '<nav class="menu"><ul class="menu__list">';

    foreach ($all_categories as $cat) {
        if ($cat->category_parent == 0) {
            $category_id = $cat->term_id;
            $menu .= '<li class="menu__group"><a href="' . get_term_link($cat->slug, 'product_cat') . '" class="menu__link">' . $cat->name . '</a>';

            $args2 = array(
                'taxonomy'     => 'product_cat',
                'child_of'     => 0,
                'parent'       => $category_id,
                'orderby'      => 'name',
                'show_count'   => 0,
                'pad_counts'   => 0,
                'hierarchical' => 1,
                'title_li'     => '',
                'hide_empty'   => 0
            );

            $sub_cats = get_categories($args2);
            if ($sub_cats) {
                $menu .= '<ul class="menu__sublist">';
                foreach ($sub_cats as $sub_category) {
                    $menu .= '<li class="menu__group"><a href="' . get_term_link($sub_category->slug, 'product_cat') . '" class="menu__link">' . $sub_category->name . '</a>';

                    // Fetch third level categories
                    $args3 = array(
                        'taxonomy'     => 'product_cat',
                        'child_of'     => 0,
                        'parent'       => $sub_category->term_id,
                        'orderby'      => 'name',
                        'show_count'   => 0,
                        'pad_counts'   => 0,
                        'hierarchical' => 1,
                        'title_li'     => '',
                        'hide_empty'   => 0
                    );

                    $third_cats = get_categories($args3);
                    if ($third_cats) {
                        $menu .= '<ul class="menu__sublist">';
                        foreach ($third_cats as $third_category) {
                            $menu .= '<li class="menu__group"><a href="' . get_term_link($third_category->slug, 'product_cat') . '" class="menu__link">' . $third_category->name . '</a>';

                            // Fetch fourth level categories
                            $args4 = array(
                                'taxonomy'     => 'product_cat',
                                'child_of'     => 0,
                                'parent'       => $third_category->term_id,
                                'orderby'      => 'name',
                                'show_count'   => 0,
                                'pad_counts'   => 0,
                                'hierarchical' => 1,
                                'title_li'     => '',
                                'hide_empty'   => 0
                            );

                            $fourth_cats = get_categories($args4);
                            if ($fourth_cats) {
                                $menu .= '<ul class="menu__sublist">';
                                foreach ($fourth_cats as $fourth_category) {
                                    $menu .= '<li class="menu__group"><a href="' . get_term_link($fourth_category->slug, 'product_cat') . '" class="menu__link">' . $fourth_category->name . '</a></li>';
                                }
                                $menu .= '</ul>';
                            }
                            $menu .= '</li>';
                        }
                        $menu .= '</ul>';
                    }
                    $menu .= '</li>';
                }
                $menu .= '</ul>';
            }
            $menu .= '</li>';
        }
    }
    $menu .= '</ul></nav>';
    
    // Enqueue the necessary styles and scripts
    wp_enqueue_style('custom-menu-style', get_template_directory_uri() . '/css/custom-menu-style.css');
    wp_enqueue_script('custom-menu-script', get_template_directory_uri() . '/js/custom-menu-script.js', array('jquery'), null, true);
    
    return $menu;
}
add_shortcode('custom_product_category_menu', 'custom_product_category_menu');

// Horozontal menu code ends here

I have given my code above. Regards