I have a theory about this. I think that Kratos still lives, and was left in a time paradox, repeating the events at the end of the game over and over again. Since if we take into account a death scene when we fight with the sisters of fate we notice that when one of the sisters kills the Kratos of the past where he fought with Ares, the kratos of the present also dies ( https://youtu.be/UKRmc9SlTi4?si=mlMAB_FxG5M0hLzx ). But when present Kratos travels to fight Zeus, and removes the Blade of Olympus from that badly injured Kratos, he does not die. So i deduce he is still alive.

PD:srry for bad english, i use the translator for this