Hi,
<em>I would like a coupon code to apply to the Total and therefore also to the Shipping costs and not only to the cart. Is this possible?</em>
I’m afraid, but WooCommerce Core, does not support that functionality:
https://woocommerce.com/document/coupon-management/#how-do-coupons-affect-shipping-calculations
Instead, you may utilize the Store Credit plugin to achieve this, although I am uncertain if it will fulfill all of your needs, but it is a work-around. The Store Credit plugin offers a general setting for applying credit towards shipping, which can be enabled for all Store Credit coupons, as explained here: https://woocommerce.com/document/woocommerce-store-credit/#apply-to-shipping.
If you have any pre-sales questions to make if it will fit your needs, you can ask them here (You might need to create an account before):
https://woocommerce.com/my-account/create-a-ticket/
Thank you for reaching out, and if you have any additional questions, please let us know.
Best ??