One possible reason could be that she is in a desperate situation. Maybe she needs something for a very important spell or potion to save someone's life and she thinks Harry won't notice or will forgive her. For example, if there is a rare ingredient that only Harry has access to and time is running out.
Maybe she's desperate for some knowledge that she thinks Harry has in those books. For example, if the books are related to some dark magic or ancient spells that she wants to study for the greater good, she might be tempted to take them without asking.
If Hermione realizes her mistake and tries to make amends, it could lead to a deeper understanding between them. They might have to work through their feelings and have some difficult conversations. For instance, Hermione might have to explain her reasons fully, and Harry would have to decide if he can forgive her.
One possible scenario could be that in this fanfiction, Harry discovers that Hermione is being bullied by some dark - minded students at Hogwarts. He steps in immediately, using his skills and the respect he has among his peers to put an end to it. Maybe he threatens the bullies with exposure to the professors if they don't stop.
Maybe Harry uses his magic skills to immobilize Ron. He could cast a spell like 'Petrificus Totalus' on Ron right when he's about to attack Hermione, thus stopping the beating.
Well, Hermione's parents could be key characters. They might be the ones who first notice Harry's odd situation when they meet him. For example, they could see that Harry seems a bit underfed and neglected, which could lead to them trying to help him in some small way. This would also give Hermione more of a connection to Harry before Hogwarts.
One key moment could be when Ron says something really hurtful in a fit of jealousy. Harry might step in immediately, telling Ron to stop and defending Hermione's honor. For example, if Ron makes a snide comment about Hermione's intelligence being overrated, Harry would firmly say that Hermione's intelligence is one of the things that has saved them all many times.
If the letter contains bad news or a problem, Hermione would likely be very concerned. She's a problem - solver, so she'd start thinking about solutions right away. For example, if Harry tells her about a new danger in the wizarding world, she'd start making plans to protect themselves and others. Her reaction would be one of determination and focus.
In this kind of fanfic, one possible scenario could be that Harry uses his quick thinking and magical skills. For example, he might use a stunning spell on the troll just in time to stop it from harming Hermione. Another scenario could be that Harry lures the troll away from Hermione, using his knowledge of the troll's behavior. Maybe he throws something noisy in the opposite direction to draw the troll's attention.