Well, one possible plot development could be that Harry uses the cane as a symbol of his new dark power. Maybe he starts to use dark magic in ways that are unexpected, like using the cane to channel dark energy for attacks. He could also start to turn against his old friends, causing a rift in the wizarding world.
One possible plot could be that Harry, feeling betrayed by the light side or lured by the power promised by the dark side, decides to join. The cane might be a symbol of his new identity or a magical tool given to him by the dark forces. He could start learning dark magic and be used to carry out their evil plans.
It could be that the cane has a connection to a powerful dark entity. When Harry holds it, he gets influenced by that entity and is drawn further into the dark side. Maybe it was crafted by a dark wizard long ago and has been waiting for the right person to use it to bring chaos.
It could be a new dark wizard who has been secretly building his power. Maybe this wizard uses the allure of the cane and the idea of a new kind of dark magic to draw Harry in. He might be a former follower of Voldemort who has his own plans for domination and sees Harry as a useful tool.
The teachers at Hogwarts, like Dumbledore (if he were still alive in the fanfic), would be deeply concerned. Dumbledore always saw great potential in Harry for good. He would probably try to understand what led Harry to this path and would use all his wisdom and magic to try and turn Harry back. The other teachers would also be on high alert, fearing for the safety of the students and the future of the wizarding world.
In such a fanfic, perhaps Harry Potter is magically manipulated. The Dark Lord could use some powerful dark magic to cloud Harry's judgment. Harry might then start to use his skills and knowledge, which were originally meant for good, to help the Dark Lord's evil plans. For example, he could use his Parseltongue ability to communicate with dark creatures for the Dark Lord's purposes.
Perhaps he was deceived. There might be a powerful dark wizard who managed to convince Harry that the dark side had a more 'just' cause. This wizard could have used false information about the history of the wizarding world and how the dark side was initially misjudged.
It completely flips it. Instead of being the hero we know, he becomes a figure of fear and suspicion. His actions would shock those who knew him, as he was always seen as the one to fight against the dark, not join it.
Dumbledore could be seen as the main antagonist from Harry's new perspective on the dark side. Dumbledore represents all that is good in the wizarding world, and if Harry has turned to the dark, Dumbledore would be the one trying to stop him, to bring him back to the light. So in this context, Dumbledore becomes the opposition that Harry has to face.
Well, perhaps Harry gets tired of being constantly in danger and feeling unappreciated in the wizarding world. He might be lured by the Dark Side with promises of power and safety. Voldemort could offer him a place by his side, showing him a different view of magic that seems more appealing in a warped way.