Issues with WooCommerce

I could not get this to work with WooCommerce Product Categories. I thought maybe because the sorting was not set to ‘menu_order’ but even setting that in pre_get_posts didn’t seem to change anything.

/**
 * Front-end Query Modifications
 * 
 * @param WP_Query $query
 * 
 * @return void
 */
function prefix_pgp( $query ) {
	
	if( is_admin() ) {
		return;
	}
	
	if( $query->is_main_query() ) {
		
		// Custom Product Order
		if( $query->is_post_type_archive( 'product' ) || $query->is_tax( 'product_cat' ) && empty( $_GET['orderby'] ) ) {
			$query->set( 'orderby', array( 'menu_order' => 'ASC', 'post_date' => 'ASC' ) );
		}
		
	}
	
}
add_action( 'pre_get_posts', 'prefix_pgp' );