Maybe the Shinigami uses its special powers to heal Naruto's severe injuries. For example, it could transfer some of its own spiritual energy to Naruto to revive his fading life force.
First off, Harry Potter would be quite disoriented in the Shinigami world. However, his inquisitive nature would drive him to explore. He'd likely start by observing the Shinigami at work. He could draw on his knowledge of the wizarding world's laws and ethics to understand the Shinigami's code. His ability to think on his feet, which he developed during his battles against the Death Eaters, would be useful when he has to make quick decisions in the Shinigami world. For example, when deciding whether to purify a Hollow or not.
Well, it could be in a crossover fanfiction where the Naruto universe combines with a supernatural world that features Shinigami. Maybe it's a story where Naruto gains Shinigami powers through some unique event or training.
One of the great Danmachi fanfics is 'A Different Perspective'. It offers a fresh take on the characters and their relationships within the Danmachi universe. The story delves deeper into the backstories of some minor characters and makes them more significant. Another good one is 'The Unseen Adventures'. It takes the characters on new quests that are not in the original story, adding more excitement and mystery.