Man, finding good stuff for the Kratos-Atreus brother dynamic is surprisingly tricky. A lot of the fics out there treat Atreus more like a son, which... yeah, obviously, but the whole Jötnar thing and the way they evolve into partners by Ragnarok opens up so much potential for a sibling vibe, especially with Kratos's own history. Like, there's this undercurrent of 'I failed my brother, but I won't fail this boy who is also my brother in arms' that doesn't get enough play.
AO3 is definitely your main hunting ground. The tagging system is crucial here. Searching just 'God of War' will bury you. You need to pair it with tags like 'Brotherly Bonding', 'Brother-Sister Relationship' (if you're into Freya & Freyr stuff, which is also stellar), or even 'Found Family'. I've had better luck filtering for the character tag 'Atreus (God of War)' and then excluding the 'Kratos/Atreus' ship tag for obvious reasons. Sometimes you find gems in the general 'Family' tag too. I remember one where an older Atreus and an angsty Thrud basically become chaotic sparring partners while Kratos and Sif just sigh in the background – it was more fun than it had any right to be.
Some writers on FanFiction.net still nail the older, pre-2018 fandom tone for the Greek-era games, which had more focus on Deimos. Those stories are a different flavor – all rage and tragedy and raw, messed-up loyalty. The Norse-era fics tend to be quieter, more about healing. Depends on what kind of sibling bond you're craving.