This bug is reported as fixed in macOS 13.1 beta. See (r. 100857507) in the release notes.
I've been following this and hoped 13.1 would address this, as I think I'm running into it.
I upgraded a Macmini9,1 to macOS 13.1 today, and made a macOS 13.1 USB installer using softwareupdate --fetch-full-installer --full-installer-version 13.1
I have a set of software permissions under Full Disk Access and other System Settings configurations (such as TeamViewer Host permissions to function).
I then took a second Macmini9,1, erased the Volume, installed 13.1 using the installer, activated, and did an install from the USB.
During setup, I migrated from a drive created with Carbon Copy Cloner that is a valid Migration source.
Everything transfers except the settings under Privacy & Settings, the TeamViewer permissions are unset, and nothing is listed under Full Disk Access.
Curious if there is something I'm overlooking, if there are any alternative ways to migrate this information, or if the official line is this is not possible.
I'm also open to the concept that this can be fixed by imaging app behavior changes due to 13.1 work, say if Carbon Copy Clone or SuperDuper! need to adjust the values they use.
For now I'm going to have to write documentation to have techs manually set up Full Disk Access for the required operation of the systems...