What is the ruling regarding the return of a wife after a single divorce, accompanied by an oath of ẓihār, and the expiration of her waiting period (ʿiddah) before the return is documented in court?

From your question, we understand that you divorced your wife with a revocable divorce (talaq raj'i), then pronounced zhihar against her during her iddah (waiting period), then took her back during her iddah, and performed the kaffarah (expiation) for zhihar, but you did not register the return (raj'ah) in court. If this is the case, then the return is valid, and your wife is under your marital bond. It is permissible for you to enjoy her company after fasting for two consecutive months. However, it is necessary to register the return in court to protect rights and avoid accusations.