How to make custom total price reactive in navigation

Using woocommerce woocommerce_add_to_cart_fragments filter you can do that.

Going by the id attribute that you currently have for the span that displays the cart total, you can use the following code

add_filter('woocommerce_add_to_cart_fragments', 'bt_update_cart_total');
function bt_update_cart_total ($fragments) {
    $fragments['#order-total-price'] = '<span id="order-total-price">' . WC()->cart->get_cart_subtotal() . '</span>';

    return $fragments;
}

Add this code to your functions.php file and thats it.