API Testing approach

I am currently working in API project where developers create unit test and BDD test after develop the service. Those both unit tests and BDD tests that developers create normally use mock instances like other external services and storage. So that they can be run as part of CI without external dependencies. Further we include all negative scenarios also under BDD.

We are working in agile space. Once the story come to testing phase what I do is create E2E BDD scenario for that story with real integration without mocking. So that we can add those E2E BDD test cases to regression suite.

I would like have your thoughts what other tests that is useful adding when story reach testing phase. Are we missing anything here?

Thanks in advance