Is the Farewell Tawaf obligatory for a pilgrim residing in Makkah after the rituals are completed, especially if he returns to Jeddah and then comes back to Makkah during the month of Hajj?

Owning a house in Mecca does not mean you are a resident unless it is a place of residence for you or you have family there. Therefore, you must perform the Farewell circumambulation (Tawaf al-Wada') when you leave it. If you perform the Farewell circumambulation and then engage in trade or residency, you must repeat it, because the Prophet (peace be upon him) said: "No one should depart until his last act is with the House."