What is it you see on the screen of the console?
If it is asking you to press the PS button, that is usually mapped to a soft sip on the center hole. The PS5 will not recognize a controller until that button is pressed.
Does it recognize button presses but not the joystick?
You can plug the Quadstick into the FGC2 and the FGC2 into a PC and go to
https://test.quadstick.com to verify the FGC2 is responding to the Quadstick. It will show up as an XBox controller to the PC.