This is using Zextras for Zimbra mobile device support.
Shared Contacts folder(s) must be visible in the Zimbra Web Client.
If you need to synchronize a shared contacts folder, you can use the CardDAV-Sync Android app. The free version seems to work well on a Samsung S20 phone.
https://play.google.com/store/apps/details?id=org.dmfs.carddav.sync
In the Zimbra Web Client:
ZWC → Contacts (tab) → <your shared contacts folder> (drop list) → Share Contacts Folder
Right-Click the URL → Copy Link Location
Add Account → CardDAV → Enter Zimbra URL and Credentials
Leave Use SSL
selected.
You can also edit Settings (gear icon) for options like: