Well, in fanfic, it could be a really interesting plot device. It might be used to create a new scenario where Harry Potter has to deal with the implications of having a federal identification in a magical world that usually operates under its own set of rules. Maybe it's used to bring the wizarding world more in line with the Muggle government systems for the sake of the story.
You could also have a plot where Harry discovers that his family has some hidden connection to a Muggle - wizarding cooperation project that requires federal identification. So, he's thrust into a situation where he has to understand this new part of his identity. He might face challenges from other wizards who oppose this new form of identification or from Muggles who don't believe a wizard should have such a thing.
I'm not sure specifically as I haven't read this particular fanfic. But generally, it might involve Bella having a federal badge and getting into various adventures or situations related to that. Maybe she uses the authority that comes with the badge to solve mysteries or face challenges in a fictional world.
In fanfic, 'harry potter has federal badge' could be a really interesting and unique concept. It might imply that Harry Potter is somehow involved with a federal - perhaps a wizarding federal - system. It could be a way to introduce new power dynamics or storylines where Harry has an official status or authority represented by the federal badge.
Maybe there are corrupt officials within the same federal system who see Bella as a threat to their illegal operations. They would try to get rid of her or stop her from uncovering their misdeeds. These antagonists would use their own power and influence within the system to create obstacles for Bella.
Since it's a fanfic, it might introduce new characters that are unique to this story. There could be a rival within the federal system who is jealous of Bella's new - found status with the badge. Or perhaps there's a mentor - like figure who has been in the federal service for a long time and helps Bella understand the ropes. Another possibility is that there are informants that Bella has to deal with. These informants could be from different backgrounds and have their own motives for helping or hindering Bella in her work with the badge.
It could work by giving Harry new responsibilities. The badge might come with certain tasks he has to fulfill, like maintaining order in the wizarding world.
Castle might become obsessed with finding the truth about what happened. His writer's mind would start formulating theories and he would stop at nothing to get justice for Beckett, which could put him in dangerous situations.
One challenge could be the state of the body. If it has been damaged or decomposed, it would be difficult to identify. Another might be the lack of proper identification tools or information at the scene. Maybe there are no fingerprints available or dental records are missing.