Should a BDD test scenario only be automated on the UI?

Commonly the answer is yes, I have a different opinion.

Let’s say feature is to show total cost of items in a shopping cart along with the shopping cart icon.

Implementation changes will be at the front end & service layer.

I’d personally want to have unit tests for new methods, component tests on the end point and:

Service integration tests for the BDD scenario – Adding / removing products to the cart and seeing if the cart total gets changed – or whatever the scenario may be

No harm in adding an extra check to an existing UI test, but I’d refrain from having a whole new UI script just for this, rather have an exclusive one on the API.