Show shipping cost but do not apply it in the final checkout total

gistfile1.txt

add_filter('woocommerce_package_rates', 'override_shipping_cost_to_zero_but_keep_label', PHP_INT_MAX, 2);

function override_shipping_cost_to_zero_but_keep_label($rates, $package) {
    foreach ($rates as $rate_id => $rate) {
        // Save original cost in the label for display
        $original_cost = wc_price($rate->cost);
        $rates[$rate_id]->label .= " (Normally $original_cost)";
        
        // Override actual cost to 0
        $rates[$rate_id]->cost = 0;
        
        // If taxes exist, zero them too
        if (!empty($rates[$rate_id]->taxes)) {
            foreach ($rates[$rate_id]->taxes as $key => $value) {
                $rates[$rate_id]->taxes[$key] = 0;
            }
        }
    }
    return $rates;
}