Is it true what is rumored about Abu Sufyan ibn Harb gloating over the Muslims on the Day of Hunayn by saying: "Their defeat will not end short of the sea," despite the existence of narrations proving his steadfastness and jihad on that day?

Abu Sufyan ibn Harb, may Allah be pleased with him, embraced Islam on the the day of the Conquest [of Mecca]. His conversion was initially somewhat coerced, but then his condition improved, and Islam took root in his heart. He fought in the Battle of Ta'if and witnessed the Battle of Yarmouk, where he encouraged jihad.

As for his statement "Their defeat will not end until they reach the sea" on the day of Hunayn, it was uttered before Islam had fully taken root in his heart.

The Abu Sufyan who remained steadfast with the Prophet, peace and blessings be upon him, on the day of Hunayn, was Abu Sufyan ibn al-Harith ibn Abd al-Muttalib, the cousin of the Messenger of Allah, peace and blessings be upon him, and his foster brother. He is not Abu Sufyan ibn Harb.