If you can get to the wiring behind the instrument panel, you can check the voltage (or resistance, I’m not sure which) on the wire from the fuel sending unit. You will need the manual to know the exact reading. If the reading when full is correct, then the problem is the gauge. If the reading is too high or too low, then the problem is the sending unit.
Google also shows a list of problems with GM fuel sensors of your vintage, with some extended warranties and repair programs. But “new GM” might have dumped them. It won’t hurt to ask at your dealer for service bulletins and any repair programs.