Why tax_query in WP_Query not working

Try to change $cat_name by the category ID.

$term_name = get_query_var('taxonomy'); // current taxonomy
$cate = get_queried_object();
$cat_id = $cate->term_id; // current category ID
    
    echo $term_name;
    echo $cat_id;
$wp_query = new WP_Query(array('post_type'=>'st_ai',
                               'post_status' => 'publish',
                               'tax_query' => array(
                                   array(
                                      'taxonomy' => $term_name,
                                      'field' => 'slug',
                                      'term' => $cat_id,
                                   )
                               )
                               ));
    
if ( $wp_query->have_posts() ) {
    echo "good";
}
?>