To export and import Site Studio configuration and any file dependencies you should use Site Studio packages. For a detailed description of the reasons behind this please see Drupal config vs Site Studio Packages.

What are Site Studio Packages?
Exported bundles of Site Studio configuration entities, file dependencies and metadata, support for this functionality is provided by the Site Studio Sync submodule. Whilst Site Studio package export and import processes are based on Drupal core configuration management it is not interchangeable due to the  additional dependency management and API interactions required by Site Studio. For more details, see Anatomy of a Site Studio package

How to export your packages