Hi Tobias,
For X, you do not have to do anything to achieve this mobile menu style as this is the default structure of the mobile menu in X.
As for Pro, the available option you have for mobile is the Navigation Collapsed element which launches and off canvas menu from the right. Changing it functionality to match the X mobile navigation would involve customization which goes beyond the scope of our support.
However, you may still use the Original Header using Pro by going to Pro > Theme Options > Header > Switch back to Original Headers. Doing so will give you the same header as X but you will not be able to customize it with the header builder.
Hope this helps.