There is no app for Carplay in iOS. It's integrated into the OS.
I have 14.7.1. Carplay works fine.
I'd try a different usb cable. I'd try the other usb port. if you haven't master reset Sync in a while, especially after multiple updates, I'd try that. Try rebooting your phone as well. Lastly, go to Cyanlabs and get Sync v. 21194. the previous two official releases had Sirius issues but also Carplay issues.