There is supposed to be a way to invite Friends (or Nearby Players) to play games that connect with Game Center, however I've been unable to get it to work. The invite goes out, but only has a link to this support page:
There's no option to Accept the invite in Messages that I can see.
And Nearby Players does not show anything. Devices are both on same WiFi with Bluetooth enabled.
As far as I can tell, I have permissions set correctly to allow either of these requests.
Accept a friend request for Game Center - Apple Support
To accept a friend request, you need a device running a recent version of iOS, iPadOS, or macOS.
support.apple.com
There's no option to Accept the invite in Messages that I can see.
And Nearby Players does not show anything. Devices are both on same WiFi with Bluetooth enabled.
As far as I can tell, I have permissions set correctly to allow either of these requests.