Despite the name, this is what actually starts the sync — it does not just close the session for bookkeeping. Call it once all products have been added with add_products_to_publish_session; it stops accepting further additions and schedules the session to be processed asynchronously. The session must currently be CREATED (i.e. not already closed, cancelled or finished). Poll get_publish_session for progress and get_publish_session_report once it reaches a terminal status.