I've restarted (a few times), as well as removed sandbox permissions (again, a few times).
In fact, I've tried a few iterations of removing sandbox permissions, uninstalled cookie, reinstalling it, and then granting full disk access (as I primarily use Safari).
As well as exporting my cookie settings (with the intent to re-import them again - however, there doesn't seem to be a lot of point if I can't even get Cookie to accept it has permissions to do its job).
It behaves as described above. Clicking on "Give global access" doesn't do anything, even after granting full disk access (and restarting, of course).