Show total savings amount in WooCommerce cart and generated order

I am using the following code to show the total savings amount in checkout page:

add_action( 'woocommerce_review_order_after_order_total', 'show_total_discount_cart_checkout', 1000 );
function show_total_discount_cart_checkout() {
    $discount_total = 0; // Initializing

    // Loop through cart items
    foreach ( WC()->cart->get_cart() as $item ) {
        $product = $item['data'];

        if ( $product->is_on_sale() ) {
            $regular_args = array( 'price' => $product->get_regular_price() );

            if ( WC()->cart->display_prices_including_tax() ) {
                $active_price    = wc_get_price_including_tax( $product );
                $regular_price   = wc_get_price_including_tax( $product, $regular_args );
            } else {
                $active_price    = wc_get_price_excluding_tax( $product );
                $regular_price   = wc_get_price_excluding_tax( $product, $regular_args );
            }
            $discount_total += ( $regular_price - $active_price ) * $item['quantity'];
        }
    }

    if ( WC()->cart->display_prices_including_tax() ) {
        $discount_total += WC()->cart->get_discount_tax();
    }

    $discount_total += WC()->cart->get_discount_total();

    if ( $discount_total > 0 ) {
        $text = __("SÄÄSTÖSI", "woocommerce");

        printf( '<tr class="total-saved"><th>%s</th><td data-title="%s">-%s</td></tr>', $text, $text, wc_price($discount_total) );
    }
}

I would like also to show taht total savings amount in cart page and in the generated order. It seems to be the order-details.php temmplate responsible for customer orders.

How to show the total savings amount in cart page and in the generated order?

There are few missing things to display also the total savings amount in cart and in the generated order.

Here below, we will save that total savings amount as custom order metadata to display the total savings amount in the customer order and email notifications.

Try the following revised code replacement:

// Utility function: Get cart total savings amount
function get_cart_total_savings() {
    $total_saved = 0; // Initializing

    // Loop through cart items
    foreach ( WC()->cart->get_cart() as $item ) {
        $product = $item['data'];

        if ( $product->is_on_sale() ) {
            $regular_args = array( 'price' => $product->get_regular_price() );

            if ( WC()->cart->display_prices_including_tax() ) {
                $active_price    = wc_get_price_including_tax( $product );
                $regular_price   = wc_get_price_including_tax( $product, $regular_args );
            } else {
                $active_price    = wc_get_price_excluding_tax( $product );
                $regular_price   = wc_get_price_excluding_tax( $product, $regular_args );
            }
            $total_saved += ( $regular_price - $active_price ) * $item['quantity'];
        }
    }

    if ( WC()->cart->display_prices_including_tax() ) {
        $total_saved += WC()->cart->get_discount_tax();
    }

    return $total_saved + WC()->cart->get_discount_total();
}

// Display total savings amount in cart and checkout pages
add_action( 'woocommerce_cart_totals_after_order_total', 'display_cart_total_savings_amount', 1000 ); // Cart
add_action( 'woocommerce_review_order_after_order_total', 'display_cart_total_savings_amount', 1000 ); // Checkout
function display_cart_total_savings_amount() {
    $total_saved = get_cart_total_savings();

    if ( $total_saved > 0 ) {
        $label = __('Savings', 'woocommerce');

        printf( '<tr class="total-saved"><th>%s</th><td data-title="%s">-%s</td></tr>', $label, $label, wc_price($total_saved) );
    }
}

// Save the total savings amount as custom order metadata
add_action( 'woocommerce_checkout_create_order', 'add_cart_total_savings_amount_metadata' );
function add_cart_total_savings_amount_metadata( $order ) {
    $total_saved = get_cart_total_savings();

    if ( $total_saved > 0 ) {
        $order->add_meta_data( 'total_saved', $total_saved, true );
    } 
}

// Display total savings amount on customer orders and email notifications
add_filter( 'woocommerce_get_order_item_totals', 'display_total_savings_on_order_item_totals', 10, 3 );
function display_total_savings_on_order_item_totals( $total_rows, $order, $tax_display ) {
    if ( $total_saved = $order->get_meta('total_saved') ) {
        $total_rows['total_saved'] = array(
            'label' =>__('Savings', 'woocommerce') . ':',
            'value' => wc_price($total_saved, array( 'currency' => $order->get_currency() )),
        );
    }
    return $total_rows;
}

Code goes in functions.php file of your child theme (or in a plugin).

In cart page:

In order received page: