Does repeating Umrah after Tawaf al-Ifadah suffice for unknowingly omitting the Sa'i of Hajj, and is the ihram for the repeated Umrah considered void due to being in the state of ihram for Hajj until its completion with Sa'i?

The question includes two issues: delaying the Tawaf al-Ifadah (circumambulation of outpouring) until after sunset on the Day of Sacrifice, and forgetting the Sa'i (ritual walking) of Hajj.

Regarding the first issue: There is no harm in delaying the Tawaf al-Ifadah, by consensus. The hadith which indicates that whoever delays the Tawaf al-Ifadah until evening becomes re-consecrated into a state of ihram is flawed in its chain of transmission and text, and it is an anomalous hadith that has been unanimously abandoned. This indicates the existence of an abrogating text, even if it is not apparent.

Regarding the second issue: The correct view is that the mutamatti' (one performing Hajj al-Tamattu') must perform two sa'is. The man's consecration for Umrah was not valid because he was still in the state of ihram for Hajj and had not yet exited from it. Therefore, his tawaf for it was considered a supererogatory act, and his sa'i was counted for his Hajj, so there is nothing due from him. Intention is not a condition for tawaf and sa'i because they are parts of a composite act of worship; the intention at the beginning is sufficient, just like in prayer. Therefore, his tawaf is valid.