After a little more investigation, it appears there is a mount point that is added when a site is added to ISPConfig, which links the log files to the log directory. I.E.
root@personal:/var/www/clients/client0# mount | grep web4
/var/log/ispconfig/httpd/test.local on /var/www/clients/client0/web4/log type none (rw,bind)
After unmounting this point, I was able to remove the directory.
Could this be worthy of a bug report, or is it simply a result of upgrading to 18.104.22.168, instead of using a clean install?