这是我最终得到的解决方案。这也可以帮助其他人。

$taxonomy = "product-category";

    $args = array(
        \'taxonomy\' => $taxonomy,
        \'orderby\' => \'name\',
        \'order\' => \'ASC\',
        \'hierarchical\'  => true,
        \'hide_empty\' => false,
    );

    $the_query = new WP_Term_Query($args);
    $categories = $the_query->get_terms();


    if ($categories){

        foreach($categories as $category){
            $ancestors = get_ancestors( $category->term_id, $taxonomy );
            $category->ancestors = $ancestors; 
            $category->depth = count( $ancestors ) ;

            if($category->depth === 3) :    

                echo $category->term_id . \'-\' . $category->depth . \'-\' . $category->name;   

            endif; 
        }   

    }   

使用的内部foreach循环get_ancestors() 函数返回包含给定对象的父对象的数组$category->depth 获取当前深度。