After sitting a couple minutes idling in hot weather a constant high pitched whine/screach comes from under the car. When I move the shifter into Neutral it stops.
With A/C on? try without A/C and see if it changes. If still happens with A/C off, check coolant valve or Inverter pump. Google it. Inverter pump easy to check. No big red triangle so far? Also does it sound from driver side wheel well area? It could be the coolant pump, if so, it is noisy. usually turns on only when you turn off the car to pump the coolant into the storage tank.
Pretty common for the HVAC system to make all kinds of weird noise in a near 20 year old Prius... As long as it keeps working, don't worry about it.
Turn off the A/C. Does it stop? Wouldn't make sense for a shift to Neutral to stop the A/C from making a noise. Only under the car? If the OP opens the hood where in the engine compartment is loudest? Something rubbing on one of the fans, or a failing fan motor, might screech. Doesn't really make sense that shifting to neutral would stop it in this case either. Very odd that shifting to neutral would silence it. Seems like it might be prudent to put a stethoscope or other listening device on the bottom of the transmission, maybe even a finger would do if the sound generates enough vibration to feel. If that is where the sound is coming from check the ATF level ASAP. There is no dipstick, the car has to be jacked up or put on a lift and a finger stuck in the fill hole after the bolt is removed.
The blow off valve on the bottom of the compressor is overfilled.. usually you see yellow dye rt under this spot under compressor.