It will turn off even when the AC is on, just not as frequently as if the AC is off. Your understanding of that was incorrect. However, it should've come back on when you either released the brake peddle, or put the truck in P. Sounds like there may be a "glitch". Refreshed model tells me it's new. It has been my experience with several GM's that "electrical gremlins" can exist after a few thousand miles. In my experience, after you have 5,000 miles on the odometer they should not happen anymore, although I've had it occur at least once after the 5,000 mile mark (but not too far after that) with my 2020 Silverado and it (cross country drive, crossing down SB I-15 into Baker, CA, cruise control set while going downhill, ESC Traction Control, CEL, and limp mode) never repeated itself after that.
If you'd like to avoid future possible occurrences you can just turn off auto start/stop when you get into the truck each time. I think there's an aftermarket device you can buy to shut it off permanently, but I don't have any info on that.