I know they charge for Artifact storage, but outside of uploaded artifacts I don't think that the logs and results of builds are billed separately?

Additionally, I thought that caching came out of a separate limit, and was not billed like artifact storage?

Lying implies intent, I don't think the person you're replying to is necessarily lying, even though they might be wrong on this specific point.

GH enterprise cloud is charging for storage separately, as an organization admin just navigate to the org admin page to see it.