What is the ruling on a man taking back his wife after a judge's divorce, and is a judge's divorce considered a completion of the three divorces?

If the judge rules to annul the marriage (فسخ النكاح), it is a revocable divorce (طلاق بائن), unless it is due to an oath of abstinence (إيلاء) or financial hardship (العسر بالنفقة), in which case it is a revocable divorce (رجعي). The judge's divorce does not count as three divorces; rather, the wife becomes lawful for him again with a new contract, provided that it was not preceded by two divorces. However, if it was preceded by two divorces, then this divorce completes the count of three, and the wife becomes irrevocably divorced (بينونة كبرى), meaning she is not lawful for him until she marries another man, he consummates the marriage with her, and then he divorces her. Reconciliation (الرجعة) is not valid before a new contract.