WooCommerce add "Save x%" next to sale prices

functions.php

<?php
// Add save percent next to sale item prices.
add_filter( 'woocommerce_sale_price_html', 'woocommerce_custom_sales_price', 10, 2 );
function woocommerce_custom_sales_price( $price, $product ) {
	$percentage = round( ( ( $product->regular_price - $product->sale_price ) / $product->regular_price ) * 100 );
	return $price . sprintf( __(' Save %s', 'woocommerce' ), $percentage . '%' );
}
?>

is it possible to do this even for different prices, variable products? !!

This code apparently doesn't work in my instance of WooCommerce Version 5.6.0, although it's been copied into the functions.php of the Storefront theme as is. Any suggestions for troubleshooting would be appreciated!

Your snippet only works on simple products. For variable products, instead, give the following code a try:

// For Variable Products Discount
add_filter( 'woocommerce_available_variation', 'custom_variation_price_saving_percentage', 10, 3 );
function custom_variation_price_saving_percentage( $data, $product, $variation ) {
$active_price = $data['display_price'];
$regular_price = $data['display_regular_price'];

if( $active_price !== $regular_price ) {
$saving_percentage = round( 100 - ( $active_price / $regular_price * 100 ), 1 ) . '%';
$data['price_html'] .= sprintf( __('You Saved: %s', 'woocommerce' ), $saving_percentage );
}
return $data;
}