Publishing your Online Store isn't quite the same as enabling it! Enabling the Online Store is to switch the actual Online Store feature on.
However, for this 'Publish' feature, it allows you to toggle whether you want your Online Store to be visible to the public or not.
Publish Online Store
To start publishing your Online Store:
Head to BackOffice > Settings > Account > Danger Zone > Publish Online Store (it's below the 'Disable Online Store' section (you will only see Publish Online Store if you have previously clicked Enabled Online Store).
To confirm, please type in PUBLISH (in capital letters) in the text field and then click 'Publish'
Note: If you wish to Unpublish your Online Store, go to BackOffice > Settings > Account > Danger Zone > press the Unpublish button.
Finally, type in UNPUBLISH (in capital letters) and then press Unpublish for the changes to be saved.