You bought the right stepper 🙂
As you say, its shaft has a diameter of 6mm. That shaft also acts as the rotation axis of the 2nd articulation.
So, the GT2 pulley that is is inserted in the shaft of that stepper motor has to be modified a little bit. You will have to expand the half of the hole of the pulley from 5mm to 6mm of diameter, in order to insert the shaft of the stepper in one side and a 5mm smooth rod in the other side of the pulley.
Here you have an image that shows what I have explained: https://cdn.hackaday.io/images/7974781470243277203.png
Also, you can check the Assembly FreeCAD file to see it more clear.
Hope it helps!