What is the Sharia ruling regarding a husband who divorced his wife verbally and left her in a state of suspension, refusing to document the divorce or restore her legitimate rights, and insists on resorting to man-made law rather than Sharia?

We can only pray for you. What your ex-husband said, that he follows the law instead of Sharia, is apostasy, and refuge is sought with Allah from that. If he took you back before your 'iddah (waiting period) ended (three menstrual cycles or three months), then you are his wife. But if it was after the 'iddah ended, then it is not permissible for him to take you back except through a new marriage contract. If you cannot prove his divorce and his failure to take you back during the 'iddah, then you can file for khul' (dissolution of marriage initiated by the wife), and this would be easier for you. We do not see it fit for you to return to him given his clear turning away from the ruling of Allah and His Messenger and his preference for the ruling of the law.