On the other hand, his experience in Tartarus could also make him more empathetic. He has endured so much pain that he might be more in tune with the suffering of others. He could be more likely to reach out to those who are in difficult situations, knowing what it's like to be in a seemingly hopeless place like Tartarus.
He could be more cautious. The perils of Tartarus might have made him less reckless. For example, he might think twice before getting into a fight or taking risks that he used to take without hesitation.
He might become more fierce. As a dragon, he has the physical power to match his temper at times. He could be less patient with those who oppose him.
It makes him more hardened. The harsh conditions force him to become tougher both physically and mentally. He has to constantly be on guard and ready to fight, which sharpens his reflexes and his ability to think quickly in dangerous situations.
It can also lead to new character development arcs for other characters. If Percy is different, those around him have to adapt. Annabeth might have to learn how to deal with this new Percy, which could be a whole new plotline in the fanfiction. Maybe she tries to bring back the old Percy, or she has to fall in love with this new version of him all over again.
His relationships with his friends could become stronger. When he eventually gets out, his friends might see him as even more of a hero for surviving Tartarus alone. They could respect him more and he might be more confident in his relationships.
His personality would likely experience a shift towards a more solemn and responsible demeanor. With godly powers come great responsibilities. Percy would no longer be able to act as carelessly as he did as a demigod. He might become more reserved in showing his emotions, especially as he realizes that his actions as a god can have far - reaching consequences. Also, his loyalty might be tested as he has to balance his new divine status with his relationships from his mortal days.
In some fanfictions, their relationship could become more complex. They might have seen sides of each other in Tartarus that they didn't expect, and it could cause some friction. But at the same time, they also have this unbreakable connection because of what they've been through. They might argue more about how to deal with the after - effects of Tartarus, like Percy wanting to just forget and move on while Annabeth wants to analyze and learn from it. However, in the end, they still love each other deeply.
He might become more cautious. Since the future is unknown and full of new things, he would have to be careful. For instance, he can't just rush into a fight without knowing what his opponents are capable of.
His confidence would likely soar. As a god, he'd know he has more power and capabilities. So he might be more assertive in his actions and decisions.
He might use his powers in creative ways to lessen the impact of the torture. For instance, if the torture involves some form of mental attack, he could try to use his connection to water to calm his mind. Also, his demigod abilities, like his superhuman strength and agility, could help him physically resist some of the more brutal forms of torture to a certain extent. And he may also draw strength from the memories of his past victories and the people he has saved.