Hi Alex,
In addition to Sarah's answer, indeed you need to add the services to the production workspace even if you did this before for the stage one. The reason why this needs to be done is simple: keeping the environments completely separated so mistakes like sending emails to real customers (when using Adobe Campaign for example) are easier avoided (because you would use the Campaign stage environment for the stage workspace and the prod one for the prod worskpace).
We will update our docs to explain this workaround. Thank you for the feedback!
Cheers,
Mihai