Can you transfer “System and network" data from a macOS High Sierra to a Catalina version macOS

Yes, either on1st boot of a new Install you can use Setup Assistant after answering a few queries.

If already setup use Migration Assistant, if you have a Time Machine drive on the 10.13 Mac move it to the newer one.

Great news, take care my friend & don't hesitate to ask if you have more questions. :)