Replace the post count on wp_list_categories with “Has Posts” instead of number and “No Posts” if none

Add the below in your theme’s functions.php. It should work the way you want

function my_list_categories( $output, $args ) {
    $output = str_replace( '(0)', '(No Posts)', $output );
    $output = preg_replace( '/\((\d+)\)/', '(Has Posts)', $output );
    return $output;
}
add_filter( 'wp_list_categories', 'my_list_categories', 10, 2 );