The part number is usually found on the side of the AC compressor pump.
7th gen Celica AC System from Toyota Celica Repair Manual vol 2
https://celicahobby.com/gallery/index.php/category/acThe same part number is used for the GT and GT-S, both manual and automatic.
The OEM ac compressor retails for about $650 USD
Part number 88320-2B420-84
#10 in the following image