As per the documentation, Draft and Private are two mutually exclusive post statuses. Therefore, when you mark a draft post as Private, it is no longer a draft.
We are a big team making extensive use of private posts. Therefore, we would like to mark a draft as private (an unfinished post that will be internal). Ideally, the "publish" button would un-draft the post, not make it public.
To put it differently, we need both a (draft / finished post) distinction, and a (public / private post) distinction.
Is that possible? Do we need a custom post status?