Since you are asking about how to do this with your own data in ArcGIS Pro, here's a summary of what you need to do: You need to create a restriction attribute that will make each road restricted by comparing the road's height limit with a parameter value indicating the height of the vehicle being modeled in the analysis. You need to set this up with a function evaluator comparing an attribute parameter representing the vehicle height against a descriptor attribute representing the height limit of the road. The descriptor attribute will probably need to use a field evaluator to draw the height limit information from a field in your street data.
The best way for you to understand how to set all this up is to run through the Create a network dataset tutorial. Part of that tutorial does exactly what I described above. The sample data that comes with the tutorial also has an already-constructed example.