Maybe it's an old enemy that Harry thought was defeated. For instance, a Death Eater who managed to survive and has developed a new form of dark magic. This dark magic is focused on mental torture and insanity. They use it on Harry, turning him into a weapon against his own friends and the wizarding community.
Another possibility is that the main antagonist could be an aspect of Harry's own mind. In the fanfiction, his subconscious fears and insecurities could be personified. This 'inner antagonist' constantly torments him, leading to his insanity. It could be his fear of not being good enough, or his guilt over the deaths that occurred during his battles, which manifest and drive him mad.
It could be a new dark wizard who has the power to manipulate minds. This wizard might target Harry specifically, driving him insane as part of a larger plan to take over the wizarding world. Since Harry is seen as a hero, if he goes insane, it would create chaos and make it easier for the antagonist to achieve his goals.
The main antagonist could be Naruto himself in a sense. Since he has gone insane, his actions are now unpredictable and harmful to the people around him. His former friends, like Sakura or Kakashi, might have to step up and try to stop him, seeing him as the new threat.
It could be a new dark wizard who has some personal vendetta against Harry. Maybe this wizard has a grudge because Harry defeated Voldemort and he wants to prove he's more powerful, which enrages Harry and causes him to go on a rampage.
The main antagonist could be a new character, a corrupt official in the Ministry of Magic who wants to get rid of Harry because he's seen as a threat to their power. This person could manipulate the legal system to send Harry to jail.
There could be a dark entity that lurks within the Durmstrang castle itself. It might have been awakened by Harry's arrival or has some connection to the school's past. This entity could manipulate students and teachers alike to create chaos and oppose Harry.
It could be a new character, perhaps a corrupt wizard in the Ministry of Magic who has a vendetta against the Dursleys for some reason. This wizard might make their time in jail even more difficult by withholding basic rights or subjecting them to unfair treatment. And he might be doing all this for his own gain, like trying to steal the Dursleys' Muggle money or something.
One possibility could be that after facing too many dark magic encounters, Harry's mind starts to break. Maybe the constant threat from Voldemort and the losses he endures, like the death of his friends, push him over the edge. He could start to have hallucinations and lose his ability to distinguish between reality and dark magic-induced illusions.
Another possibility is that an evil wizard from the past, who was previously defeated, gets resurrected or empowered by Harry's time - traveling interference. This wizard could then become the main antagonist, using Harry's actions to their advantage and wreaking havoc on the wizarding world.
There might be a character who is secretly from the wizarding world but has turned to the dark side. This character could be after Harry in the Ouran setting, trying to use the chaos of the new environment to their advantage to get to Harry without being noticed by the Hogwarts professors.
It could be a new dark wizard that we haven't seen in the original series. This wizard might be jealous of Harry's fame and power and wants to eliminate him by making him disappear.
A jealous classmate could be the main antagonist. This person might be envious of Harry's popularity or the strange things that seem to always work out for him. They could start spreading rumors or trying to trip him up in his studies.