I think the point is that no one in particular bears the guilt for the crucifixion due to some really unfortunately timing to be born at a certain era. People will be judged for their sin, but no one specifically for this act this day. He's doing a "presidential pardon," so to speak. Even though they haven't asked for forgiveness, they are being granted amnesty for this act.

Why is he saying, "Father, forgive them" instead of "I forgive you"? Those who were executed were supposed to say, “May my death atone for all my sins,” but Jesus confesses instead the sin of those who falsely convicted him, who under OT law were liable for his penalty before God.

Regarding why "if the only way to be saved is by seeking Jesus," this forgiveness of Jesus is not in any way pertaining to their salvation, but to this specific incident.

Why did Jesus pray for the forgiveness of those who persecuted him? In Luke 23:34, Jesus prays for those who crucified him, "Father, forgive them, for they do not know what they are doing." I understand the obvious here... that Jesus is forgiving and loving, even all the way to death. However... according to orthodox doctrine, the only way to be saved is to make the choice for yourself. How can Jesus be praying for the forgiveness of those who aren't seeking forgiveness? And why is he saying, "Father forgive them" instead of "I forgive you," if the only way to be saved is by seeking Jesus?