Where is the Key Port for the Gen III 2010 prius?

There is no key port for the 2010. The directions are in the Owner's Manual on page 541 and copied below.

Apply the brakes and touch the Toyota emblem side of the
electronic key to the “POWER†switch.
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An alarm will sound to indicate that the start function cannot
detect the electronic key that is touched to the “POWER†switch if
any of the doors is opened and closed while the key is touched to
the switch.
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To change “POWER†switch modes: Within 10 seconds of the
buzzer sounding, release the brake pedal and press the
“POWER†switch. Modes can be changed each time the
switch is pressed. (​

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→P. 162)

To start the hybrid system: Press the “POWER†switch within
10 seconds after the buzzer sounds, keeping the brake pedal
depressed.

In the event that the “POWER†switch still cannot be operated, contact your Toyota dealer.​

ITO52P165​

STEP ​

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Thats all true, once your inside the car, you can use the RFID in the smart key to start the car without any transmission from your smartkey, but the actual metal key that pops out is to unlock the drivers door to get you inside assuming your transmitter is dead, in which case you will need to use the above method to start the car.