I see the same issue about invalid permissions of /var/log/apt-cacher-ng when installing the latest package on bookworm.
I installed it multiple times on this VM before without this issue, not sure why it started to fail in this way now. Somehow the /var/log/apt-cacher-ng directory has owner = "root", no manual intervention was done as far as I am aware. When apt-cacher-ng package is installed it fails with the error about permission on /var/log/apt-cacher-ng folder. Could it be some sort of regression via some other package which adjusts permission of files in /var/log? apt-cacher-ng does not seem to have had any release lately so no regression there. Could either the installation of the package perform a check and fix or the systemd service could adjust access rights during startup to make apt-cacher-ng more robust against such invalid permissions?