Torah Temimah cites Yoma 36a.
“And he shall confess” — confession with the offering.
Diyuk pairing vidui with the korban process — confession is integral to the offering’s atonement sequence.
Confession is part of the atonement process of this section, spoken over the offering. The words and the blood-service form a single unit of kaparah. Separating vidui from the korban would leave the verbal acknowledgment without its sacrificial counterpart and the offering without its verbal acknowledgment of the specific sin.