In such a fanfiction, Harry Potter believing he's a Jedi could lead to a lot of chaos and confusion in the wizarding world. He might start using his wand like a lightsaber, trying to deflect spells as if they were blaster bolts. His Hogwarts professors would be very puzzled by his new behavior. He could also start to look for ancient Jedi texts in the Hogwarts library, thinking that there is some connection between the magic of the Jedi and the magic of the wizarding world.
Hermione would probably be very skeptical at first. She'd try to find logical explanations for Harry's new belief. Ron, on the other hand, might be a bit more open - minded or just find it really funny. He could make jokes about Harry using his wand as a lightsaber. His other friends like Neville might be a bit confused but also supportive in their own way, waiting to see what Harry does next.
One possibility is that Harry starts having dreams about being a Jedi. He might start using his magic in ways that mimic Jedi powers, like using his wand as a sort of lightsaber. He could try to find other 'Jedi' in the wizarding world, thinking they are like him.
Maybe Harry uses his magic skills like the Patronus charm to protect the Jedi from the Sith. His ability to apparate could also help Jedi in quick escapes.
A possible plot could be that a Harry Potter character discovers an ancient magic that has similarities to the Force. They then start to develop abilities and a moral code similar to Grey Jedi. They might face opposition from both the wizarding world, which is used to the traditional light and dark magic, and some dark forces that see this new power as a threat.
The plot of such a fanfiction could be really intricate. Imagine Harry Potter suddenly realizing that he can sense a different kind of energy, the Force. He starts to explore this new power secretly, fearing how others in the wizarding world would react. As a grey Jedi, he has the freedom to use the Force in ways that are not strictly light or dark. He could use his powers to enhance his magic, for example, using Force - enhanced speed to be quicker in Quidditch. He would then get involved in a conflict that requires both his wizarding skills and his new Jedi abilities. Maybe Voldemort has some connection to a dark side Force user, and Harry has to use his grey Jedi knowledge to defeat this new threat. Along the way, he would have to make difficult choices about how to use his powers, and this could lead to some tense moments with his friends and mentors in the wizarding world.
One possible plot could be that during one of his adventures outside of Hogwarts, Harry stumbles upon a strange object that turns out to be a zanpakuto. He has no idea what it is at first, but as he starts to explore its powers, he realizes it has a connection to a different kind of magic. He then has to learn how to use it while still dealing with the threats in the wizarding world, like Voldemort and his Death Eaters.
One possible plot could be that Harry is cursed by a dark wizard, and as a result, he grows snake hair. He then has to deal with the reactions of his friends and teachers at Hogwarts. Some might be afraid of him, while others try to find a way to break the curse.
A fanfiction could start with Harry's glasses being stolen by a mischievous house - elf. Harry starts to squint to see in his classes, which causes some problems. For instance, in Potions class, he misreads the instructions and creates a minor explosion. He spends the day trying to find the house - elf and his glasses. Along the way, he meets some other characters who help him in unexpected ways. By the end of the day, he gets his glasses back and has learned a valuable lesson about not taking his eyesight for granted.
One possible plot could be that Harry's insanity is caused by a cursed object. His friends then have to find a way to break the curse while also dealing with his erratic behavior. For example, Harry might accidentally reveal secrets to the wrong people because of his insanity.
The plot could involve Harry struggling to hide his true nature as a Nathrezim from his friends at Hogwarts. He might have new, dark powers that he has to learn to control, and he's afraid of how others will react if they find out. Meanwhile, Voldemort senses something different about Harry and is both intrigued and threatened by him.