Strange, I have PoE hats on a number of my Pi's (Kodi and OctoPrint) one of which (OctoPrint) has a Raspberry Pi Camera (V2), it works flawlessly. Only thing that appears to be different is I'm using a Netgear FS726TP SmartSwitch with PoE.
According to the switch status the port is delivering 55.5V at 68mA (3.7W). This goes up to 106mA if I use a USB port on the Pi to power an SKR V1.3 with a TFT35-E3 touch screen.
Maybe it's an issue with your switch? Might be worth (a) checking the cable and (b) trying a PoE Midspan Injector.
The only relevant tweak I have in my config.txt is
# Tweak the fan parameters - see: https://github.com/raspberrypi/firmware ... ADME#L1804
Which raises the temperature at which the fan runs slightly (stops it being annoying when the pi is mounted on the back of a telly!)