We have the same problem and have not yet received a satisfactory answer or solution from Apple Support. I also don't understand why this shouldn't be technically possible. The App Store Connect API documentation claims that "The roles that apply to keys are the same roles that apply to users on your team." (see https://developer.apple.com/documentation/appstoreconnectapi/creating_api_keys_for_app_store_connect_api). But this is not true, the role "Customer Support" cannot be assigned to the API key. So for the "Respond to customer reviews" permission, only the "Admin" role can be used, but this would unnecessarily give the API key a lot of powers. I hope that Apple will soon become aware of this problem and provide a solution quickly.