Sample code for getting url
jQuery(document).on('ready', function() {
var variant = $('select.product-single__variants :selected').val();
console.log( variant );
var loc = window.location;
var origin = location.origin;
var pathname = location.pathname;
var finalUrl = origin + pathname + "?variant=" + variant;
//updating URL
history.pushState({}, null, finalUrl);
});
Sample code for reload a section
$(".product__price-and-badge .product__price").load(finalUrl+" .product__price-and-badge .product__price>*","");