Hi there, good question. There are a couple things in play that could affect the answer.
First, and working backwards, marking the API design as `published` is the best way to say "done".
Next, there is no "official status field" inside the definition structure, but I have found the info/description field to be the best place to put "in your face" status. You can use Markdown to make bold, or even to embed an image in the description, which could indicate the status in your workflow.
Finally, comments and resolution of comments is a good way to indicate state (I know you said in lieu of comments, but just saying). You can use them as sign-off based on different needs.
I hope that helps, and please post back any other questions or details of your needs.