In the following sentence, why is perfect conditional used instead of present conditional

From the Economist(soft paywalled)

The well-respected senator, who said he was stepping down because of “mounting health challenges”, would not otherwise have been up for re-election until 2022, when he would probably have kept his seat.

The author was describing a future unreal event. According to what I learned in high school, he should have used present conditional instead of perfect conditional, which is used to describe unreal events in the past.

The well-respected senator....otherwise would not be up for re-election...when he would probably keep his seat.

I always find conditionals very hard to grasp while learning English. I don't know if I made a mistake or if the venerable TE did. Thanks for your time.

Solution 1:

The well-respected senator, who said he was stepping down because of “mounting health challenges”, would not otherwise have been up for re-election until 2022, when he would probably have kept his seat.

The entire sentence is in the past tense.

If he had not said he was stepping down, he would not have been up for re-election until 2022.

That's the implication: He had said + would not have been.

The had said is implied.