Is it obligatory for us to wait for the Friday Prayer after completing the Farewell Tawaf and Ifadah on a Friday, an hour before the Dhuhr Adhan, or should we depart from Makkah?

Whoever finishes the Farewell Circumambulation (Tawaf al-Wada') before the time for Friday prayer begins is not obligated to wait for the Friday prayer, nor to depart Makkah before its time commences. He has the choice between traveling before its time begins or performing the Friday prayer and then traveling. However, if there is a long separation between the Farewell Circumambulation and the performance of the Friday prayer, then the circumambulation should be repeated. What is mentioned in the question is not considered a long separation.