In almost every org I’ve been in, E2E meant full thickness UI to datastore and back tests. That’s where I was coming from.
I’ve never considered the single service tests E2E, more either a component test suite or a public API unit test suite (same thing).
I agree you’d want those with collaborators mocked, and it’s where I’d lean the bulk of my test strategy for a system like that from a QA POV (as well as promoting internal API unit testing from a dev POV).