There's also 'The Demigod and the Death Note'. It could explore how the characters from Percy Jackson would react to the existence of the Death Note. Maybe Percy or Annabeth would have strong moral objections to the power of the Death Note and try to destroy it, while facing off against the likes of Light Yagami.
In some fanfics, a plot twist might be that the Death Note has some sort of connection to the Greek underworld. Maybe it was created by Hades as a way to control the souls in a different way, and when Light Yagami starts using it, he unknowingly disrupts the balance between the mortal world and the underworld. This could lead to Percy and his friends having to step in and deal with both Light and the chaos in the underworld.
Yes, there are likely some fanfictions out there with the concept of 'Percy Jackson is death'. Fanfiction writers often come up with unique and creative interpretations of existing characters. You can start by looking on popular fanfiction websites like Archive of Our Own or FanFiction.net.
In some fanfictions where Sally dies, it could lead to Percy being filled with a new kind of rage and determination. He might become more withdrawn at first, shutting out his friends as he grapples with the loss. But eventually, it could fuel his growth as a hero, making him more fearless in the face of danger because he has already lost the most important person to him.
Nico di Angelo has a strong connection to the Underworld, so he's a prime candidate. He can already communicate with the dead and has some control over the shadows, which are related to death in a way. In fanfiction, he could be further developed to become the Master of Death, perhaps by making a deal with Hades or finding a hidden power within himself.
Another common opponent could be other demigods from different cabins. For instance, a child of Ares who might have a more aggressive and straightforward fighting style compared to Percy. This would create an interesting dynamic as they have different powers and personalities but are still on the same side in the general scheme of things.
Maybe he faced an extremely powerful enemy that he couldn't overcome. It could be a new and terrifying monster created by the Titans or some other dark force.
Annabeth could be a strong ally. She's always been by Percy's side, and her intelligence would be crucial in helping Percy navigate his new role as the son of death. She could research ancient texts to find out more about the powers and responsibilities that come with it.
Ryuk would probably just be amused. He is a Shinigami who has seen a lot in his existence. Fanfiction is just another strange human creation to him. He might chuckle at some of the more outlandish ideas in the fanfictions, like a character having superpowers beyond the Death Note.
Misa would likely be excited. She is a big fan of Light and the whole 'Kira' concept. In fanfiction, if there are scenarios where she has more power or a closer relationship with Light, she would be all for it. However, she might also get jealous if there are other female characters getting too close to Light in the fanfictions.