I have a 2017 Denali and we experienced what you are speaking of while traveling to FL 1.5 years ago. I would command A/C and got muggy 83F air instead. I checked over all the fuses because I always travel with tools. Everything OK. Commanded A/C on with hood open - no clutch engagement. Key cycled a few times - no change.
Continued on my not-merry way at that point and all of a sudden I had cold air. It worked flawlessly for the rest of the trip. On the way home, the radio lost it's mind and would change stations, skip songs, etc. The screen was whacking out and I got video of it. The only reason this is relevant to the story is because the A/C controls and radio are all one piece when replaced by GM.
I have great friends that really know their stuff in northern IL. Since I bought the extended warranty, I had it looked at and explained the issues. They replaced the entire radio and climate control piece (comes as one unit). It has worked perfectly since then.......up until last week and the A/C didn't turn on when commanded, but did after a short bit. The radio then started playing from my wife's phone when I unlocked the truck and opened the door after hiking. SO, now I get to see if GM's 2 yr 24,000 mile warranty is good on repairs.
Long story short, I'd get a second opinion from a dealership that has more experienced techs.