He might be like a fish out of water at first. But gradually, he'll find his place. Maybe he'll use his unique skills to help Annabeth with her school projects.
She'd fit in by being herself. Her intelligence would make her a great addition to the academic scene. She could participate in debates and win them easily.
She might focus on her studies more. Since Annabeth is really into knowledge, she could pour all her energy into her schoolwork, like spending extra hours in the library or on research projects.
She might initially be shocked. Annabeth is a strong character, so she could start by trying to stand up to Percy verbally, asking him why he's being so mean.
She could start by being honest with Percy about her feelings. Just come clean and say why she wants to get back together. For example, she might say she realized she can't live without him. This straightforward approach might help Percy see that she is sincere.
He could become withdrawn. Percy is a sensitive person at heart. So if Annabeth's actions are really hurtful, like if she cheats on him in a fanfic (although it's a very sad scenario), he would likely isolate himself from her and their friends. He might go off on his own to think things through and deal with his pain privately.
Annabeth might be initially in awe of Percy's new godly status. But she would quickly start thinking about how to use this new situation to their advantage. She is practical, so she would likely start planning how they can better protect their friends and the world.
At first, it might become strained. Annabeth could be hurt and pull away from Percy. She might not want to be around him as much.
She might be initially very angry. Annabeth is intelligent and perceptive, so she would likely feel betrayed that Percy thought he could deceive her. For example, if Percy lies about a mission, she could find out the truth later and confront him immediately, demanding an explanation.
Another way is through the intervention of their friends. Their mutual friends could bring them together and encourage them to see things from the other's perspective. The friends can share stories about how each of them is really a good person deep down. This might soften their hearts towards each other.
One possible fanfic could be about Percy and Annabeth facing a new mystery in high school. Maybe there's a strange teacher who seems to know more about their demigod past than they're comfortable with. Percy could be struggling with his ADHD in the academic setting, and Annabeth is constantly helping him study while also trying to solve the mystery of the teacher.