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”.
Publish to Server Method 1
From the Server Menu
From the Server menu on the menu bar, there is an option to “Publish Data Source”.
Publish to Server Method 2
There you are. Spoilt for choice.