The Volturi could be a main antagonist. They might see the intrusion of the wizarding world into their territory as a threat to their power and secrecy. They could try to eliminate Harry Potter and Charlie Swan to protect their vampire - centric world in Forks.
It could be Voldemort. Even though he's from the Harry Potter universe, if he finds out that Harry is hiding in Forks, he could send his Death Eaters there. This would not only put Harry in danger but also the Cullens and the people of Forks as the Death Eaters might start causing chaos.
Perhaps there's a spell gone wrong that links the Twilight world and the Harry Potter world. Charlie Swan and Harry Potter find themselves in a situation where they have to reverse the spell. They encounter various characters from both universes. Charlie has to learn about the wizarding world quickly, and Harry has to deal with the strange vampire and werewolf dynamics in Forks. They face challenges like dealing with the Volturi who see the magical intrusion as a threat, and at the same time, they have to find a way to send everyone back to their respective worlds.
The mummy itself could be the main antagonist. It could be a mummy that was once an evil sorcerer in ancient Egypt, and now that it has been awakened, it wants to spread its dark magic and rule over both the Muggle and wizarding worlds.
Obviously, Slenderman could be the main antagonist. His spooky nature and his ability to cause fear and disappearances would make him a perfect fit for the role. He could be trying to spread his influence over the wizarding world, which would put him in direct conflict with Harry and his friends.
It could be Voldemort still. Imagine Ares coming into the Harry Potter world, and Voldemort seeing this as a threat to his own power. He would try to either eliminate Ares or use him for his own dark purposes. Ares, on the other hand, may not take kindly to Voldemort's evil ways and so they become enemies, with Harry in the middle trying to defeat Voldemort while also keeping Ares in check.
It could be the school bully. In the context of their relationship, the bully might target Charlie Brown specifically when he's with Heather, trying to embarrass him in front of her. This could create tension in their relationship as Charlie Brown might start to avoid Heather to protect her from the bully's taunts.
Yes, there are some out there. You can start by looking on fanfiction websites like Archive of Our Own. Some fanfictions might explore the unique relationship between a character from Harry Potter and Charlie from Twilight, perhaps in a crossover adventure where they team up to face a common threat or solve a mystery that spans both their magical worlds.
Maybe a new character that is created specifically for this fanfiction. This character could be jealous of the attention fem Bowser is getting from both the wizarding world and Harry Potter's group. They could start causing trouble and trying to turn everyone against fem Bowser. This new antagonist could also have some connection to Bowser's original world, perhaps an enemy from there who has followed her to the Harry Potter universe.
It could still be Voldemort. Since he is the main villain in the original Harry Potter series, in this fanfiction he would see the Goddess Lemon as a threat to his plans of taking over the wizarding world. He might try to eliminate her before she can fully use her powers to help Harry and the Order of the Phoenix.
Another option could be a corrupted version of Merlin. What if he was turned evil by some dark magic? He would know all the secrets of both the Arthurian and wizarding worlds. He could use this knowledge to create chaos and try to rule over both. Harry and the good knights of Arthur would have to find a way to reverse his corruption.