The only thing I really know about F-Droid Basic is that it supports auto updates without manual confirmation on Android 12+, and the start screen is a list of the latest updated apps.
Auto updates are awesome and work completely unattended in the background, just like an app store should work.
Iirc CalyxOS ships F-Droid by default and did include the F-Droid privileged extension, which enables unattended updates. This extension has to be installed in the system, which isn't possible on stock ROMs.
They probably saw F-Droid Basic as a solution to no longer having to ship the privileged extension. I don't think CalyxOS is shipping Aurora Store by default, but it also needed a privileged extension (until they supported the new unattended update mechanism two years ago).