Buy a new head unit... increasing the sound quality and adding the Bluetooth at the same time (also add in front and rear cameras). Adding the steering wheel controls to the right won’t add Bluetooth as that’s a “delete item” on many build sheets (was on mine).
I would recommend getting a new steering wheel Do to ease and cosmetic reasons (only about $200) or if on a budget, adding the right side controls to the steering wheel for volume, source select, and calling features. Not worth the time adding a factory GM module thats already 10 year old technology and sounds like crap.
It’s a good idea to get to know your PPV by heading to any GM dealership and having them run your VIN on their “Work Bench” software and print out the build sheet. They did it for free for me and took minutes.