At the moment Thunderbird does not use native vCard 4.0 elements to define address lists, and so they can not be synced via CardDAV and do not export correctly to a file that can be interpreted as a list by other clients.
Using the member attribute (and KIND:group) would solve this problem (if the server also does vCard 4)
See vCard RFC: https://www.rfc-editor.org/rfc/rfc6350.html#section-6.6.5
And also: https://bugzilla.mozilla.org/show_bug.cgi?id=1668791#c8