After finding out that I cannot create a new network dataset from scratch in ArcPro (which is a real bummer!) I created one in ArcCatalog, created a template, and created a new dataset from this template (to simulate the workflow for customers of us). Now in the original network dataset I have the option that I can add restrictions but not in the one created from the template.
Why is that and how can I solve this? The data structure is for both networks the same with a feature dataset of 5 road classes plus the junctions.
EDIT: I played around a bit and added bus lines and bus stops to the network dataset and changed the group connectivity - and voilà: I have the options available. But maybe someone can tell me what exactly made me not having the options available before?