In some interpretations, one possible crime could be his manipulation of Harry Potter. He knew Harry was a tool to defeat Voldemort from the start and perhaps didn't fully disclose this to Harry, leading Harry into a dangerous life without his full knowledge.
Another aspect could be related to his handling of the secrets within Hogwarts. He may have been aware of certain dark happenings, like the secrets in the Chamber of Secrets, but didn't take enough preventative measures. This could be seen as negligence which might be considered a crime in the context of the fanfiction.
It could be Harry Potter himself. After realizing how he had been used, Harry might decide to hold Dumbledore accountable. Harry has the power and the motivation, having been through so much due to Dumbledore's actions or inactions.
It's also possible that Dumbledore has been misinformed or is under the influence of a dark spell himself. In the wizarding world, there are many forces at play. He could have received false information that made him think this was the best course of action for Harry. Another aspect could be that he is trying to teach Harry a lesson in a very extreme way. Maybe Harry has been too reckless, and Dumbledore wants to make him understand the seriousness of the situation.
Perhaps Dumbledore foresaw some sort of prophecy that was related to Harry and his parents. In order to fulfill the prophecy in the right way or to avoid a greater catastrophe, he kept Harry from his parents. He was always thinking about the greater good of the wizarding world and might have believed this was a necessary step.
Perhaps there are safety concerns for the students that Dumbledore is not addressing adequately. Harry, having a strong sense of responsibility for his fellow students, may feel that the only way to ensure their safety is to remove Dumbledore from his position. He might believe that Dumbledore's actions or inactions are putting the students at risk, and thus he takes matters into his own hands.
Well, it could be that Harry has a different view on how to handle the war against Voldemort. Dumbledore is often very strategic and sometimes keeps things from Harry for what he believes is the greater good. But Harry might think that full transparency is necessary. Also, Harry may have formed new alliances or friendships that give him different perspectives, and these new ideas conflict with Dumbledore's. He might feel that Dumbledore's approach is too old - fashioned or risky in a new context.
One possible motive could be protection. Dumbledore might tie Harry to the bed to keep him from running off into danger. He has always been protective of Harry and perhaps in this fanfiction's unique scenario, he believes this extreme measure is necessary to safeguard Harry from some immediate and unseen threat.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
One possible reason could be a misunderstanding. Maybe Harry overheard something that made him think Dumbledore was planning something against him that he didn't understand. For example, if he heard Dumbledore discussing a dangerous mission for him without his full knowledge.
In a more extreme case in the fanfiction, Dumbledore might assign Hermione to a special project that is both difficult and dangerous as a form of punishment. For example, he could send her to study a group of cursed magical creatures in the Forbidden Forest. This would be a punishment that not only tests her skills but also her courage.
The fanfiction could focus on Dumbledore's backstory. Fans might write about his early years at Hogwarts as a student, his friendships, and how he developed into the great wizard he became. It could also include his interactions with other magical creatures in more depth than the original series, such as having secret meetings with centaurs or merpeople to gain wisdom.