Without seeing a wiring diagram it’s difficult to comment but in general most modern cars have a main relay that controls power to most of the ancillary stuff (stereo, heater, lights) and then their own relays to turn them on and off. If it’s the main relay that’s shorted it could affect multiple things.
As the heater was on even with the key off then either it was the main relay they’ve changed or if there’s be just changed the heater relay there is something wrong with the main relay or the power circuit as well.