One possibility could be that in the fanfiction, Jon Snow discovers the Valyrian steel in an ancient castle's armory. Maybe it was hidden away for centuries, and his discovery sets off a chain of events that changes the course of his journey.
It's highly unlikely that the characters in 'House of the Dragon' would actually watch fanfiction about themselves. Fanfiction exists in our world, created by fans for fans, and the characters in the show are fictional entities within their own fictional universe. They don't have access to the fan - created stories about them.
Valyrian Steel could be part of an ancient prophecy in the Harry Potter fanfiction. Maybe it's said that only a wizard with a pure heart and a connection to the founders can wield a weapon made of Valyrian Steel. Harry, being the hero, is destined to find and use it to defeat the ultimate evil. It could also be that the Valyrian Steel is hidden in a different magical realm that Harry has to travel to, which would introduce new and exciting settings into the fanfiction.
Definitely not a true story. House of the Dragon is a work of imagination and creativity. It weaves a complex tale of power, politics, and dragons within a fictional realm.
He could use it to defeat a powerful enemy. Valyrian steel is very effective against certain threats in the 'Game of Thrones' universe. So, when Jon Snow finds it in the fanfiction, he might be able to slay a great foe that was previously unbeatable.
The Legend of the Dragon King is a manga. We know that this manga is about the Legend of the Dragon King of Douluo Continent 3. It told the story of the protagonist, Xiao Lin, who was reborn in another world and became a mangaka, challenging the legend of the Dragon King. However, apart from this basic information, we are unable to obtain more detailed information about the manga.