When you plug the Quadstick into the FGC2, it does not power up??
But it powers up ok when connected directly to the PS5?
What are the lights on the FGC2 doing?
I am wondering if something went wrong with the firmware update for the FGC2. Try another FGC2 firmware update. Try a different version of the firmware.
You can also plug the FGC2 into a PC/Mac and watch its outputs change on a site like
https://test.quadstick.com. It should appear as an XBox 360 controller on those hosts when not in programming mode.
Do not have the quadstick, or anything else, connected to the FGC2 input during firmware updates.