Perhaps in the 'new death note story', the Shinigami who are associated with the Death Note have changed their ways. They could be interfering more directly in the human world, either to protect the Death Note or to stop its misuse. This would add a whole new layer of conflict as humans would have to deal not only with the power of the Death Note but also with the meddling Shinigami.
It could be a young detective who is trying to solve the mystery of the Death Note's reappearance. He might be really smart and determined to stop whoever is using the Death Note for evil purposes.
A 'Death Note Love Story' could be centered around two characters who are on opposite sides of the fight over the Death Note. One might be a Kira supporter and the other against Kira. Their love could develop as they see different aspects of each other through their battles. It could show how love can grow even in a world filled with death and power struggles brought about by the Death Note.
In the Death Note story, there's this notebook that falls into Light's hands. He starts his 'cleansing' of the world by writing the names of wrongdoers. However, as he does this, the authorities, led by the brilliant L, start to suspect someone is behind these strange deaths. It's a complex story full of moral dilemmas as Light believes he is doing good, but his actions are still taking lives in a rather unethical way. There are also Shinigamis in the story, death gods who own the Death Notes.
It focuses on the story of L's early days and how he solves cases. In this novel, we see L's unique detective methods and his battle of wits against various criminals.
Maybe in this fanfic, the world of Gotham and the world of Death Note collide. The Shinigami start to appear in Gotham, which causes mass panic. Batman starts to investigate these strange supernatural beings. He discovers the Death Note and realizes its power. He then has to figure out how to stop the Shinigami from causing chaos in his city and also prevent any humans from using the Death Note to kill others, as it would lead to a complete breakdown of the already fragile justice system in Gotham.
The plot might involve Sakura being in a moral dilemma. Since she's a healer in the Naruto world, using the Death Note which is a tool for killing would go against her nature. So, it could be about how she struggles with this new power that she has and tries to find a way to use it without sacrificing her values.
Maybe the kidnappers are actually Kira supporters. They kidnap L because they see him as a threat to their 'god' Kira. L could use his deduction skills even in captivity. He might start a mental battle with his kidnappers, trying to make them slip up and reveal information about Kira's identity or their own motives.
One possible plot could be that Light Yagami discovers the existence of demons from the Inuyasha world. He might see them as a new type of 'evil' to be eradicated. He could start using the Death Note on demons, which would draw the attention of Inuyasha and his group. Inuyasha would initially be confused about these strange deaths and then realize that a human is causing them. This would lead to a conflict as Inuyasha believes in slaying demons in a more 'honorable' way and not through this strange notebook's power.
The 'Death Note BB Novel' mainly focuses on the story of Beyond Birthday. It delves into his twisted nature and his use of the Death Note in his own devious ways. It shows his battles of wits and his attempts to outsmart others while using the power of the Death Note for his own rather cruel and unethical purposes.
I'm not sure yet as it's a new story. But it could be new characters who discover the Death Note, or perhaps some descendants of the original characters like Light or L.