It could also inspire some characters to open up about their own insecurities. If Percy, who seems so tough, can break down, it might give others the courage to share their own fears and doubts.
Maybe he's missing his family. He's been away from them for a long time on the Argo 2, and homesickness could hit hard and make him cry.
When Percy joins Kronos in the fanfiction, it affects the other characters in many ways. Chiron, the centaur mentor, would be deeply disappointed. He had so much hope for Percy. The minor demigods who looked up to Percy would be lost. They might lose faith in the idea of being a hero. The relationships that Percy had built over the years would be shattered. His joining Kronos would also make the enemy stronger, which would put more pressure on the remaining good characters to come up with a plan to stop them both.
The hunters of Artemis might be caught in the middle. They respect Artemis but also might see Percy as a valuable ally. So, they could be torn between trying to appease Artemis' jealousy and maintaining a good relationship with Percy. For example, some hunters might distance themselves from Percy to avoid Artemis' wrath.
It could make other characters who are involved in the hunt feel conflicted. For example, if some of his friends are part of the hunt, they might feel guilty or try to change Percy's view.
His friends would be devastated. They rely on Percy in many ways, and his sudden absence would leave a big void. For instance, Annabeth might feel lost without him, as they have a deep connection. She would probably be very worried and try to find him.
It can limit Percy's growth as a character. If Artemis is always protecting him, he might not get to face challenges on his own and develop fully. Other characters might feel sidelined because Artemis is so focused on Percy. For example, some of Percy's friends who also want to help him might find it hard to get involved if Artemis is constantly stepping in.
It could cause a rift among the characters. Some might think he's being selfish by secluding himself, while others might understand his need for privacy. This difference in opinion can create tension and arguments within the group. Also, if Percy has an important role in the group, his absence could make it difficult for the group to function properly in certain situations.
His friends might be divided. Some who are more inclined to support Olympus might be at odds with Percy. For example, Annabeth, who has a certain respect for the gods, could face a dilemma in choosing between Percy and Olympus.
Jason is likely to be another main character. Since he has his own set of skills and knowledge, he might have an interesting relationship with Percy in this story. Maybe he's a bit jealous at first of Percy's control over the ship, but then they end up working together really well. And of course, Piper could be there too. She might use her charm - speak abilities to help the crew communicate with any strange creatures they encounter during Percy's time controlling the Argo 2.
He might start yelling. Percy is known for his passionate nature, so when angry on the Argo 2, he could raise his voice at those who he thinks are at fault.