Hello Heellaquie37
Good day & welcome.
The SBB site and app just get me nowhere.
Yes, for a good reason as there is no possibility to import your Swiss Half Fare Card (not half fare pass) into the SBB Mobile app when it has been purchased through a third-party reseller.
You could have purchased it through SBB, then it would appear in the SBB Mobile app.
As for now, simply use the PDF document together with your physical passport or identity card (no images of it on smart phones, no photo copies, both are not accepted).
To activate the half fare option when purchasing tickets, read here:
https://community.sbb-tickets.cc/d/26418-how-can-i-save-the-info-of-swiss-half-fare-card
Kind regards,
Roland