Q: When do I actually need to buy a new set of TPMS?

Mainly when you build a second set of wheels, like a dedicated winter or off-road setup, since each set of wheels needs its own sensors. You would also replace them when the internal batteries eventually die after several years. Building a fresh set of wheels such as the UP.FIT Forged PD wheel and tire package is the usual reason to buy four. Mounting new rubber on the wheels you already own is not, since those sensors are still in there.