Reflect default price and strikethrough in cart item price in WooCommerce

I have added a progressive pricing based on the quantity of each cart item. What I am struggling with, is to reflect the $default_price from the product (instead the now manually added price) and also to set the layout of the new price like this (default_price has strikethrough):

add_action( 'woocommerce_before_calculate_totals', 'add_custom_price', 20, 1);
function add_custom_price( $cart ) {

    if ( is_admin() && ! defined( 'DOING_AJAX' ) )
        return;

    foreach ( $cart->get_cart() as $item ) {
        $quantity = $item['quantity'];
        $discount_price = 0.008333333333;
        $default_price = 4.25;
        $minimum = 10;
        $maximum = 100;
        if( $quantity > $minimum ) {
            if( $quantity > $maximum ) {
                $new_price =  $default_price - ($discount_price * ($maximum - $minimum));
            }
            else {
                $new_price = $default_price - ($discount_price * ($quantity - $minimum));   
            }
        $item['data']->set_price( '<del>' . $default_price . '</del> <strong>' . $new_price . '</strong>');
        }
    }
}

The coded $item['data']->set_price( '<del>' . $default_price . '</del> <strong>' . $new_price . '</strong>'); is wrong, but how do I reflect this so it can accept the html elements?

For what you wish to obtain you can use the following:

• While the woocommerce_before_calculate_totals action hook is used to calculate totals

• The woocommerce_cart_item_price filter hook ensures the strikethrough of the original price.

• explanation via comment tags added in the code

function action_woocommerce_before_calculate_totals( $cart ) {
    if ( is_admin() && ! defined( 'DOING_AJAX' ) )
        return;

    if ( did_action( 'woocommerce_before_calculate_totals' ) >= 2 )
        return;

    // Settings
    $discount_price = 0.008333333333;
    $minimum = 10;
    $maximum = 100;

    // Iterating though each cart items
    foreach ( $cart->get_cart() as $cart_item_key => $cart_item ) {
        // Product quantity in cart
        $quantity = $cart_item['quantity'];
      
        // Quantity greater than minimum
        if ( $quantity > $minimum ) {
            // Default price
            $default_price = $cart_item['data']->get_price();
            
            // Quantity greater than maximum
            if ( $quantity > $maximum ) {
                $new_price =  $default_price - ( $discount_price * ( $maximum - $minimum ) );
            } else {
                $new_price = $default_price - ( $discount_price * ( $quantity - $minimum ) );   
            }
            
            // Set price
            $cart_item['data']->set_price( $new_price );
        }
    }
}
add_action( 'woocommerce_before_calculate_totals', 'action_woocommerce_before_calculate_totals', 10, 1 );

function filter_woocommerce_cart_item_price( $price_html, $cart_item, $cart_item_key ) {
    // Get the product object
    $product = $cart_item['data'];
    
    // Is a WC product
    if ( is_a( $product, 'WC_Product' ) ) {
        // Get reqular price
        $regular_price = $product->get_regular_price();
        
        // New price
        $new_price = $cart_item['data']->get_price();
        
        // NOT empty and NOT equal
        if ( ! empty ( $regular_price ) && $regular_price != $new_price ) {
            // Output
            $price_html = '<del>' . wc_price( $regular_price ) . '</del> <ins>' . wc_price( $new_price ) . '</ins>';        
        }
    }

    return $price_html;
}
add_filter( 'woocommerce_cart_item_price', 'filter_woocommerce_cart_item_price', 10, 3 );