For better integration between 5.x (symfony based) kernel and legacy (4.x) kernel, injection is used to inject settings, session and current siteaccess from 5.x into legacy using an event: kernel.event_subscriber
Injected siteaccess
When Exponential legacy (4.x kernel and extensions) are running via the new Exponential 5 kernel, then the 5.x Siteaccess is injected into it to avoid having to match twice and maintain two set of matching rules.
To configure siteaccess in your Exponential 5 setup, look to the 5.x documentation of Siteaccess matching.