As with so many (maybe all!) things in Tableau, there is more than one way to publish a data source to Tableau Server. Here are two:
Right clicking on the data source
Right click directly on the data source icon and a menu will appear offering you the option to “Publish to Server”.
From the Server Menu
From the Server menu on the menu bar, there is an option to “Publish Data Source”.
There you are. Spoilt for choice.