This may be entirely unrelated - I know almost nothing of these matters - but there are a couple of things I'd like to tell in case they're helpful in diagnosing this scenario...
I upgraded by 2017 iMac to Ventura (from Monterey) once Apple had released 13.1 I immediately ran into a couple of issues with other software I use - Mail Steward (MS) and Carbon Copy Cloner (CCC). Both of these need the permissions turned on for full disk access and accessibility...
In the case of MS, my issue was that my once-a-day schedule didn't run after the upgrade. Eventually, another user told the developer (John Seward) that he'd had success by granting the permissions and immediately rebooting. Further, this was only required in a situation where MS had been installed prior to the OS upgrade - a cleanly installed MS into a machine already running Ventura didn't display this behaviour. This worked for me -my scheduled MS archival routine has run perfectly ever since. John's "best guess is that it is a bug in Ventura that causes the OS to not notice a new scheduling plist file until it is rebooted."
In the case of CCC, their support told me to manually set the permissions in System Settings (I'm just getting the hang of the new naming conventions!) rather than rely on applying the settings from within CCC itself. They said, "Typically macOS will grant CCC's helper tool full disk access as long as you have granted full disk access to "Carbon Copy Cloner", but we've found that to be terribly inconsistent. It's more consistent to explicitly grant full disk access to CCC's helper tool."
HTH and HNY,
Tim.