You can find how to attach a life-cycle to a created service in G-Reg from here. After following it once you promote the service until it gets to the production state, then you can publish that service as an API. And then you can see your created API from api-publisher app.
However note that when you are trying to change the created API status as 'published' from publisher-app, as explained in your mentioned documentation, it contains the known bug as APIMANAGER-834. We are currently working on a fix for this issue.