His relationships with his friends from Camp Half - Blood might become strained as he's away from them for long periods. They could worry about him and feel left out of his new adventures.
His life changes a great deal. He's in a whole new environment filled with gods and goddesses. He no longer has to worry about hiding his demigod status as much. He has access to a lot more resources, like the magical items that the gods possess.
His relationship with Annabeth might be more strained. Since he grew up in the wild, he would be less accustomed to the structured world of Camp Half - Blood where Annabeth thrives. They might have a harder time understanding each other's ways of life at first.
With his friends at Camp Half - Blood, Percy might become a bit of an outlier. His connection to Zeus through the blessing could make some of his friends who are more closely tied to Poseidon or other gods feel a bit uneasy. However, it could also earn him respect from those who admire Zeus' power. Percy would have to work hard to maintain his friendships while dealing with this new dynamic.
In a 'Percy Jackson Father of Chaos' fanfiction, Percy's relationships would be in upheaval. His friendship with Grover would face a test. Grover, who has always been Percy's loyal friend, would now have to deal with a Percy who is unpredictable at times. Percy might accidentally cause chaos that affects Grover's nature - related tasks. With the other demigods at Camp Half - Blood, Percy would become a sort of enigma. Some would look up to him as a new kind of hero, while others would be jealous of his new - found power. His relationship with the sea gods, like Poseidon, would also change. Poseidon might be proud that his son has such a powerful new role, but also worried about how Percy will use his powers and how it will reflect on the sea god's domain.
His relationship with Annabeth would change. She might be a bit jealous at first of Percy's new connection to Hecate. But then she would see how his new powers could be useful. They would have to learn to work together in a new way, with Percy having different abilities to bring to the table. His friendships with other demigods like Grover would also be different. Grover might be a bit in awe of Percy's new magical side. Percy would also have to form new relationships with the followers of Hecate, who might be very different from the demigods he's used to.
His relationship with Annabeth would be really interesting. If Percy is reincarnated as Theseus, he might be more headstrong in his decision - making, which could cause some friction with Annabeth who is used to the normal Percy. For example, in planning a mission, Percy (as Theseus) might make a bold move without consulting her first.
When it comes to his relationship with Hera herself, it would be complex. At first, Percy might be resentful or confused about being adopted by her. But as time goes on, he might start to understand her in a way no one else does. Hera could start to see Percy as a true son, and this could lead to a deep, if somewhat unusual, bond between them. Percy would have to balance this new relationship with his existing ones, and it could lead to some really interesting character development and story arcs.
Percy's relationship with the other campers at Camp Half - Blood would be a rollercoaster. The children of Poseidon might feel a bit betrayed or confused, as they thought Percy was one of their own. However, Percy could use his new status to bridge gaps between different cabins. For example, he could work with the children of Aphrodite to improve relationships in the camp, since Hera has some connection to love and relationships in a different way than Aphrodite. With the gods, his relationship with Zeus would be extremely strained, given Zeus's past issues with Hera. But he might find new allies among the gods who are friendly with Hera, like Hephaestus. Overall, Percy's relationships would be a mix of challenges and new opportunities.
Percy's relationship with the male demigods would change significantly. Some might see him as a traitor for joining the Hunters. However, he would also gain new allies among the Hunters themselves. His relationship with Artemis would be that of a mentee and mentor at first, but as time goes on, it could develop into a more family - like bond. And his relationship with the gods would be different too, as he's now under Artemis's protection, which might make some gods view him in a new light.
Percy could discover ancient and forgotten temples or shrines in the wild. These could hold powerful artifacts or be the lairs of minor gods or spirits. He might have to face various traps and puzzles to explore them fully. In the process, he would rely on his skills as a demigod, like his ability to control water, to overcome obstacles and uncover secrets. This would be an exciting addition to the fanfiction as it would add new elements to the Percy Jackson universe.