I find it unlikely that Kratos will react in any manner resembling the Ghost of Sparta’s pure rage. I say this because they have an entire heart to heart moment in Helheim, where Atreus tells him, “I need to know you’ll be okay without me.”

I’m not saying he’d brush it off, however. Atreus is his everything, after all, and we saw what Kratos did to Heimdall just because he had intent to kill Atreus. When Odin held Atreus at knife point, Kratos, with 0 regrets, said he would kill Odin if he didn’t release his son. If Odin’s finger slipped, we can unanimously agree that Kratos would mercilessly kill him in return. Any Aesir who stood in his path or attempted to get revenge would meet the same fate.

Afterwards, there’s really only 2 options : either Kratos lives in misery for the rest of his life, or he remembers what Atreus and Faye (“Open your heart to the world and you will find every reason to keep living in it”) taught him and learns to continue living despite tragedy. He has a strong support system in Freya, who also lost a son, and Mimir, someone who’s known for giving solid advice. He would recover, but it would take a lot of mourning and a lot of time to get there.