I just noticed that the documentation of the machines API is wrong or outdated:
No response body is wrong, the response body is
{"previous_state":"stopped","migrated":false,"new_host":""}.
Why do you have 2 different documentation pages for the API? The one at https://fly.io/docs is up-to-date for start-machine endpoint.
Having multiple sources of truth saying different things seems like a bad idea to me.