Also got a 2021 Silverado, I haven't had issues about it disconnecting but I do have the issue where my music sounds choppy. What I've figured out so far is that if I leave the truck with my phone and come back, the choppy music starting happening. There is two ways that I've figured out how to fix it; 1) restarting the truck or 2) switching to radio for like 30 seconds and then back to carplay (works most of the time).
I'm taking the truck into the dealer on Monday for rear leaking window problem and I told them to check out the carplay as well. So I'll hopefully have some more info mid/late next week.