MWTraveltoSwitz
A half fare card is NOT a prerequisite for buying discounted tickets. Anyone could do that, as the card is not cross-checked during ticket purchase.
Also you can’t “add” the 1-month Swiss half fare card (intended for foreign visitors) to the app. Such instructions you might have found relate to the similar Half Fare Travelcard, which is a yearly subscription-based product intended for residents.
You only need the half fare card during a ticket control in the train, to prove that you are entitled to travel with a discounted ticket, instead of full fare.