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I am asking this question again (posted by another user) because I think this is such a basic and obvious need, what we would call back home a "no-brainer".
By default the WebDAV connector is configured to access the collaboration areas of Nuxeo, which are at the moment the Workspace areas. This is the reason why no access has been given to sections through WebDAV.
SearchRootBackend contains the query defining this aspect:
SearchRootBackend
SELECT * FROM Workspace WHERE ecm:mixinType <> 'HiddenInNavigation' AND ecm:currentLifeCycleState <> 'deleted' AND ecm:isProxy = 0 ORDER BY ecm:path
To change this behavior you have to write an subclass with another query, create a factory equivalent to SearchBackendFactory to instantiate your class, and contribute this new factory through the backendFactory extension point.
SearchBackendFactory