Are other web analytics being logged? Is "Track referring local pages" enabled in Settings > On-line marketing > Web analytics?
When you test this, can you see the CMSUserPage cookie in your browser? This is used for a lot of the Web Analytics functionality. In order to log a referringsite_local, this cookie needs to have a LastPageNodeID and it must be different from the NodeID of the current page.
If you don't see this cookie, try checking your cookie levels (https://docs.kentico.com/k11/configuring-kentico/adding-cookie-law-consent-to-web-pages/cookie-levels). The CMSUserPage cookie has a cookie level of Visitor (https://docs.kentico.com/k11/configuring-kentico/adding-cookie-law-consent-to-web-pages/reference-kentico-cookies).
Also, check the Event Log and your browser's console (F12) for errors.