What’s the url queryvar for a taxnomy archive?

I think you can use the below code-

$terms = get_terms( array(
    'taxonomy' => $_GET['taxonomy'], // It will get the taxonomy name from HTTP get variable.
    'hide_empty' => false, // If you need to hide the empty taxonomy or not.
) );

Now the $terms will be an array if there is any taxonomy or taxonomies other wise it will through a WP_Error instance. Run a foreach loop and decorate it as your wish. For more information read this.