On the AWStats configuration when you enable the plugins for GeoIP, the relevant lines remains commented in the AWStats configuration file for the domain, so the plugin won’t run.
My solution was to add those lines to the etc/awstas/awstats.conf.local global configuration file.
Thanks for the information! I use now GeoLite2 like you. It took me a lot of time to find the required Geo2 libraries, so I add a link to a page that has installing instructions for different operating systems (mine is the “Debian/Ubuntu 20+ / Debian 10+”.