Hello jlourenco
No, the Swiss Travel Pass *IS* your ticket. You only need additional tickets for stretches where the STP is not fully covering the travel, see the STP validity map here: Swiss Travel Pass validity, download a PDF map
As a general rule, Swiss trains use a free seating system; a seat reservation is only mandatory for Glacier Express, Gotthard Panorama Express, and GoldenPass Express, or international trains to Italy. On IC, EC, ICE trains, however, seat reservations are optionally possible within Switzerland but often not required.
Kind regards,
Roland