Now I'm on the last chapter, but chapter 4 had another moment which is why I think rage and the barbarian class is suitable for Conan
With a terrible cry he heaved upward hurling the stone aside. The winged one came on again, and Conan sprang to meet it, his veins on fire with madness. The thews started out like cords on his forearms as he swung his great sword, pivoting on his heel with the force of the sweeping arc. Just above the hips it caught the hurtling shape, and the knotted legs fell one way, the torso another as the blade sheared clear through its hairy body.
See, to me, everyone else is focused on the beserker rage of the barbarian, in Conan it was called the red mist, but to me this passage reads like a rage attack, maybe even reckless attack. So many things that Conan has done in the stories fit the 5e barbarian class in my mind. It doesn't always mean frothing at the mouth berserk. I recall another moment where he's fighting someone stronger than himself but he managed to overcome them which I see as raging which grants advantage on strength checks.
Meanwhile, I don't see him as having many, or any, levels in thief rogue. He may have needed it in the past for the perce tile thief skills, but he was never rogue-like, his skills of climbing and stealth were a result of his Cimmerian upbringing, not thieving. He tends to brute force his way through locks, cutting them in half with his sword rather than finessing the lock.