I finally found out how to do this.
The key is the “persistence” tool window. Apparently it is made available after you add the JPA facet, but is a separate tool window.
To open it : menu “view” -> Tool Windows -> Persistence
In this window you see your application with the different persistence related elements (I see persistence.xml, entityManagerFactory from Spring context, and myUnit which I don’t know where it comes from.
Here you can right-click on any element and choose “Assign data source”.
This opens a pop-up dialog with a small table containing you persistence elements on the left column and the data source assigned to it on the right column. You can assign a datasource from the “Database” window in there, so I picked the datasource I had configured for my MySQL DB and voilà, the validation errors went away.
But if I enter a wrong table or column name, I still get an error, which is pretty neat.