Just left the Genius bar and got the word that there is no way to ever regress the OS. The recovery os auto updates to the newest version and requires internet to initiate installation.
If you're using Apple Silicon, you need to boot into 1TR (hold down the power button during boot) and enable Reduced Security mode. The Genius Bar probably isn't going to tell you about that sort of thing.
Thank you for this suggestion . The genius bar was less than helpful. I have reduced security selected and still I am given a “Ventura is not compatible with this mac” dialog. I made a usb installer with 13.0 and it didnt work so I just assumed the worst. this new 13.0.1 usb i just made also does not work. I tried turning of sip as well. Both the developer line and genius bar say apple does not support rolling back the OS. I find documentation though indicating reduced security allows installing older versions. Im not sure what I am doing wrong.
What I know for sure is that Reduced Security mode turns off the online "phone home" check you described in the OP, but I don't actually know what issue you're encountering.