It might be a story about his family, not just his own past but also about Atreus' mother. Kratos could be sharing memories of their life together, how they met, and the kind of person she was. This would give Atreus a deeper connection to his family heritage and a better understanding of his own identity.
After the main story of God of War Ragnarok, Atreus is in a position where he has a lot of potential for growth. His experiences during Ragnarok have no doubt changed him. He may be seeking to use his knowledge and skills for the betterment of the realms. For example, he could be using his understanding of the languages and cultures he's encountered to broker peace between warring factions. He also has to deal with the fact that he is now more aware of his godly nature and the responsibilities that come with it. This could lead him to make choices that not only affect himself but also the entire cosmos.
One common theme is growth. Both Kratos and Atreus are constantly evolving in their abilities and understanding of the world around them. Fanfictions often explore how they grow individually and as a team.
Atreus may embark on an adventure to find other beings like him, those who are of mixed heritage. He could be searching for answers about how to balance his two natures - the godly and the giant. Along the way, he may encounter challenges such as facing powerful enemies who oppose his very existence or trying to solve complex riddles left behind by the ancient races. His adventures could also involve him making new allies, perhaps from species that were previously unknown to him. And he might have to use his wits and new - found powers to overcome the obstacles in his path.
Sure. One popular fanfiction might be about their further adventures in new, uncharted lands. It could explore how Atreus grows even more in his skills and wisdom under Kratos' guidance.
The story Kratos told Atreus might have been about his journey to redemption and the lessons he learned along the way. Maybe it included details of the difficult choices he had to make and the consequences of his actions.