Using that analogy, obviously Jesus and St. Paul thought that the Father is vengeful and the Holy Spirit is merciful.
Why?
Because Jesus says that He’s sending the Holy Spirit to be our advocate, and St. Paul says that the Holy Spirit intercedes for us in groans too deep for words. Neither of them said that the Father was going to do anything like that, so obviously they were dismissing the First Person of the Trinity.
Sigh.
And yes, it is routine in ancient Christian art and sermons to picture Jesus as the Righteous Judge, and to picture the Holy Spirit as the Advocate of Sinners. The idea is not that Jesus is mean. The idea is that God is both just and merciful.
The alternate way to portray this many-sided more-than-fairness of God is to picture the saints as our advocates, or even to picture the saints or patriarchs as our just accusers, but Jesus letting people into Heaven anyway.
These are not supposed to be some kind of exquisitely balanced theological lecture. They’re supposed to be encouragement to sinners.
But of course, we do know from the Bible that the saints will act as judges of angels, and that the Apostles will sit judging the Twelve Tribes of Israel. And we do know that God apparently likes to give humans a role in all His divine works – not because He needs to, but because He likes to let His adopted sons and daughters have responsibilities, too.
We also know that God did lessen His punishments on Israel, in Jeremiah’s time, with reference to the weeping of Rachel being heard and rewarded. Obviously God didn’t need Rachel to tell Him that Israel needed help; but He chose to include her.
So the stories are not necessarily all that far off from what will happen at Judgment.