Another aspect could be the emergence of new magical laws or lack thereof. Without the Ministry to enforce regulations, magic could be used more freely, but also more dangerously. Some wizards might start experimenting with dark magic without fear of punishment, while others would strive to create a new, more just system of governance from the ground up.
Harry Potter himself would likely be a central figure. He has a history of fighting against dark forces and would probably step up to try and maintain order. Hermione would also be important as she is intelligent and could come up with plans to deal with the situation. Ron, with his loyalty and courage, would be by their side.
Perhaps he uncovers some major corruption or inefficiency in the Ministry. So, as a result of his efforts to reform it, he is given control. For example, if he finds that the Ministry has been misusing magic for personal gains, he could lead a movement to take it over and run it in a more just way.
He might openly oppose their policies. For example, if the Ministry tries to pass a law that restricts the use of certain spells for self - defense, Harry could publicly speak out against it, giving interviews or writing articles in wizarding newspapers.
One possible reason could be the Ministry's corruption. In the original series, the Ministry often showed signs of being influenced by dark forces or being overly bureaucratic and not seeing the real threats. So in the fanfiction, this might be a driving factor for Harry to oppose them.
Well, in some fanfictions, Harry Potter might come to own the Ministry of Magic through his heroic deeds. He could have defeated a great evil that threatened the wizarding world so severely that the wizarding community decides he is the most fit to take over and reform the Ministry.
Hermione could be a key character. She is always by Harry's side, and her intelligence and knowledge of the wizarding laws would be invaluable in the lawsuit. She might be the one doing all the research and preparing the legal arguments for Harry.
His friends from Hogwarts like Hermione and Ron would most likely support him. They have always been by his side through thick and thin in the original story, so in the fanfiction, they would continue to support Harry in his fight against the Ministry.
The Order of the Phoenix members might also back Harry. They've fought against the dark forces before and if they see that the Ministry has become a threat, they'd side with Harry. Dumbledore's old allies in the Order would believe in Harry's judgment and join him in his mission to destroy the corrupt Ministry.
Maybe the ministry reads Harry Potter fanfiction because they are interested in the creativity of the fans. Fanfiction can offer new perspectives on the existing story, and they could find some interesting concepts that could potentially be incorporated into their own understanding or even the official wizarding world in some way. Also, it could be a way for them to monitor if there are any dangerous or subversive ideas floating around in the fan - created stories.