We do only show the status in context=edit (ref).
This has been reported at least one other time in testing. I think it's a bit silly not to include status: we support querying for a post status unauthenticated, even if just for the default status of publish (ref) or inherit for attachments (ref).
Another status-related issue: It's not possible to query posts with the inherit status unauthenticated. But, it looks like they may show up in /wp/v2/posts if read permission is otherwise allowed. Needs some testing.