Coupon redemption form
I finally figured out the answer: the functionality has simply not been coded. Applying the patch from this issue: https://www.drupal.org/node/2792653 (patch #95 is the latest right now) will add a checkout pane for entering coupon codes. It is still not available on the cart page as you would expect in a webshop, but at least visitors can enter a coupon code.

You can place the checkout pane using Commerce->Configuration->Checkout flows->pick your flow by clicking 'edit'->Coupon redemption pane.