Yeah its definetly the design of the rubber pad that sits on the wireless charger, i have the same issue with my 2022 Sierra At4 refresh with my s22 ultra it would fast charge for a second, the slow charge then stop & just keep cycling over and over whether it was in or out of a case. I thought it was a faulty wireless charger at first after i tried it with my girlfriends s22 Ultra a few days later & it did the same thing. The next day i tested it with my cousins iphone 12 proMax and it worked fine, same with my dads iphone 13. Ended up going to another dealer and testing the charger on a 2023 silverado rst & it did the same thing with my s22ultra so i knew it was just the design.
I Took the rubber pad up like you suggested and it wireless fast charged fine for 30 min in its case, I'm guessing the rubber foot on the bottom of the pad that lets the AC airflow cool the pad is just a tiny bit too thick and is pushing some of the bigger or newer phones to the edge of wireless charging range.