I am having trouble adding the parent category to my URL in this code snippet. Any help would be appreciated.

Code is to show categories underneath products in woocommerce.

remove_action( 'woocommerce_shop_loop_item_title', 'woocommerce_template_loop_product_title', 10 );
add_action( 'woocommerce_shop_loop_item_title', 'VS_woo_loop_product_title', 10 );
 
function VS_woo_loop_product_title() {
    echo '<h3>' . get_the_title() . '</h3>';
    $terms = get_the_terms( $post->ID, 'product_cat' );
    if ( $terms && ! is_wp_error( $terms ) ) :
    // only displayed if the product has at least one category
        $cat_links = array();
    foreach ( $terms as $term ) {
        $cat_links[] = '<a href="'.esc_url( home_url() ).'/product-category/'.$term->slug.'">'.$term->name.'</a>';
    }
    $on_cat = join( ", ", $cat_links );
    ?>
    <div class="label-group">
        <div class="categories-link"><?php echo $on_cat; ?></div>
    </div>
<?php endif;
}