TL;DR — follow ALL of the instructions
And… sure enough… page 372 (" 6.Sign out of your Apple ID on all testing devices and sign back in with your new sandbox tester account.")
Was the minor detail I missed… I had signed into Game Center in the app, but didn’t do it on the simulator main iCloud account.
Now If I can just figure out what the ^%$^&%$ thing is on a yellow background
(actually, that looks like a simulator bug… looks fine on the iPhone simulator) (apparently a known bug on Big Sur on iMac)