This Name and Photo Sharing feature is proprietary and does not have anything to do with CardDAV directly. I think if you sync your Contacts in your iCloud (with ADP enabled), your Contact info is still unencrypted.

As far as I know, it‘s like the Share Name and Photo feature of iMessage, which is end-to-end encrypted. What algorithm they use, is unclear. I suppose it‘s similar to how Signal profiles work.