If you need to set a CSS class on change checkout stepwise then follow the below instructions.

You need to override progress-bar.js from

vendor/magento/module-checkout/view/frontend/web/js/view

to your current theme and replace the below js function.

/**
 * @param {Object} item
 * @return {*|Boolean}
 */
isProcessed: function (item) {
 var itemCode = item.code;
 if (itemCode == "shipping") {
 jQuery('body').addClass('payment-step');
 jQuery('body').removeClass('shipping-step');
 } else {
 jQuery('body').addClass('shipping-step');
 jQuery('body').removeClass('payment-step');
 }
 return stepNavigator.isProcessed(item.code);
}