The woocommerce_cart_product_price filter runs with the admin flag set because WooCommerce uses admin-ajax.php to generate the mini-cart. The custom_price() function in class-wc-custom-price-label.php just returns the price if is_admin(), so the price label doesn’t show in the mini-cart. Changing the check for admin as below allows the price to display with labels in the minicart too.
if ( is_admin() && !doing_filter('woocommerce_cart_product_price') ) {
return $price;
}