We have implemented Webex App with UCM calling. Only users are searchable from within Webex. Shared / common area contacts are not assigned to a user and therefore not listed.
Once you have configured Directory Connector it becomes the single source of truth for Webex identities. Therefore there is no option to sync shared / common area contacts from CUCM into webex.
If these contacts must be sourced from Active Directory can the Directory Connector be extended to sync AD "Contacts" into Webex?