Typical Prius sounds as soon as car is turned off

Most likely the inverter coolant pump or the brake pump running. Both completely normal to hear.

 

One sound probably is the engine coolant heat recovery system pump running. This will typically run upon cold startup as well as upon shutdown, for several seconds at a time. The purpose of this system is to speed up engine warmup, for the sake of reduced exhaust emissions.

Another sound may be the brake pressure accumulator pump, which will periodically run throughout the time that the Prius is READY and may even run when the car is IG-OFF. To force the pump to run so that you can recognize the sound, just make the car READY then repeatedly pump the brake pedal until you hear the pump run.

The inverter coolant pump runs continuously while the Prius is IG-ON or READY, and this sounds like an aquarium pump. This is located behind the driver's side headlamp assembly and normally runs quietly enough so that you will not hear it unless you open the hood and listen for it when the gasoline engine is not running.

The inverter makes a high-pitched sound when the Prius is READY. The sound increases in volume when you decelerate the vehicle.