Hello Christian,
I did test and I can see that there’s no notification but the product was added on the cart.
You could try testing for a plugin conflict. You can do this by deactivating all third party plugins, and seeing if the problem remains. If it’s fixed, you’ll know a plugin caused the problem, and you can narrow down which one by reactivating them one at a time. If this is not cause by a plugin, please provide admin credentials on a private reply so we can check your settings.