I had a quick look and GM doesn't seem to make their own gasoline stabilizer - they make a fuel conditioner that's meant for cleaning fuel injectors etc. but not the antioxidants and corrosion inhibitors that a fuel stabilizer has. "Corvette Forum" has some discussion on it, most people use Sta-bil or similar products made by other companies. They also mention Sta-bil 360 which is meant to reduce issues with ethanol fuels, but the info I found on that stuff doesn't say anything about using it as a storage additive. Sta-bil has been around for decades, used by a zillion people, and I didn't find anything negative about it, so I think we're on pretty safe ground with it - but you do want to use the correct amount, and follow the instructions to ensure it gets mixed properly with the gas in your tank.
Best practice is to use a fresh tank of Premium gas, which has higher additive treat rates, and, at least where I am, typically will have less or no ethanol in it, and keep the tank full to minimize tank vapor space "breathing". Add Sta-bil during your last tank fill, to let it circulate through the fuel system before you put the car to bed.
By the way: I've never had any luck with the goofy pre-measuring gizmo on the bottle - so try it out first, or use a funnel (in addition to the one that came with your car to add gas with a jerry can) or you may end up with half of it on the side of your car when you try to pour it into the tank
just sayin'