He would probably start to see the world in a different way. Since Hephaestus skills involve a deep understanding of mechanics and construction, Percy might start noticing the weak points in buildings and how things are put together. This could be useful not only in battles but also in his daily adventures. He could use his newfound skills to repair things quickly or even modify existing structures to make them more defensible. Also, he could communicate better with the Hephaestus cabin kids, sharing ideas and learning from them about different crafting techniques.
His water - based powers could be enhanced in a unique way. He might be able to shape water into more complex and intricate forms, like forging water - made tools or weapons, similar to how Hephaestus forges metal. This would be a new and interesting addition to his existing abilities.
Well, one possible plot could be that Percy discovers his new relation to Hephaestus later in his adventures. He might then start to have an affinity for creating and fixing magical items, which could be a new skill for him in battles against monsters. He could also meet other descendants of Hephaestus who teach him more about his heritage.
A possible main antagonist could be a rogue Hephaestus - related creature. Maybe a mechanical monster that Hephaestus created long ago but it went out of control. It could be targeting Percy specifically because of his new - found relation to Hephaestus, seeing him as a threat to its own existence or purpose.
Percy could be accidentally caught in the middle of their relationship drama. For example, Aphrodite might use Percy as a way to make Hephaestus jealous. Or Hephaestus could mistake Percy's innocent interactions with Aphrodite as something more, and Percy has to prove his innocence while also trying not to get too involved in their godly relationship issues.
In the 'Percy Jackson Disappears' fanfiction, perhaps Percy could be kidnapped by an unknown enemy. Maybe it's a new villain who has a vendetta against the demigods. This would lead to his friends, like Annabeth, going on a desperate search for him, facing many dangerous challenges along the way.
In fanfiction, Percy could be in the hospital because he was captured by an enemy and tortured. Now he's there being healed by the camp's healers or some advanced demigod medical technology. Another possibility is that he's having some sort of identity crisis related to his demigod status and it's causing him physical and mental stress, so he's in the hospital for both medical and psychological help.
One common theme is Hephaestus' role in helping Percy with his quests. Since Hephaestus is the god of blacksmiths and craftsmen, he might provide Percy with a special weapon or tool. Another theme is the exploration of Hephaestus' relationship with his children in the context of Percy's interactions with them. For example, how Percy might help a Hephaestus - descended character come to terms with their heritage.
Well, in this fanfiction, Percy's immortality could lead to some really interesting character development. He may start to feel lonely as he realizes that he will outlive all of his friends. This could cause him to be more withdrawn at first. But then, as he interacts with the students at Westover Hall, he might find new meaning in his immortality. He could start to see it as a way to protect others not just for a short time, but for as long as he exists. He could also form deep and lasting friendships with those who accept him for who he is, regardless of his immortality.
In the fanfiction, Percy might face new challenges related to his demigod status. Maybe he has to deal with the aftermath of the war, like rebuilding Camp Half - Blood or helping new demigods adjust.
I think Tyson, Percy's cyclops half - brother, would be a good character. His strength and loyalty would be assets in any situation. Also, Nico di Angelo could be in the fanfic. His control over the dead could provide an interesting dynamic, especially if they are exploring some dark or ancient places related to Hephaestus' past works. And of course, Clarisse La Rue. Her combat skills and fierce personality would add some drama and action to the story.