Percy would most likely go into a state of panic. His mind would be racing, thinking about all the teasing he'll get from his friends and what his mother would say if she found out. He might try to make a joke to ease the tension, but it would probably come out all wrong. Annabeth would be a bit more calm, but still mortified. She would be thinking about how this could affect their reputation in the camp, especially since they are both leaders in a way. She might give Percy a look that says 'this is all your fault' even if it wasn't really.
In the fanfiction world, if Percy and Annabeth were caught kissing, it could lead to various reactions. Their friends might tease them mercilessly. For example, Grover could make some funny goat - like noises and give them knowing looks. It could also create some tension within the group if there are those who secretly have feelings for either Percy or Annabeth. Maybe some would be jealous or feel left out. Another possibility is that their relationship becomes more public knowledge, which could have both positive and negative impacts. On one hand, they might get more support from their friends who are happy for them. On the other hand, it could attract the attention of enemies who might try to use their relationship against them.
Yes, there are likely many fanfictions out there with this scenario. Fanfiction websites like Archive of Our Own (AO3) and FanFiction.net probably have numerous stories about Percy and Annabeth where they are caught kissing. You can search using their names and relevant keywords on these platforms to find such fanfictions.
One possible plot could be that they are in a restricted area of Camp Half - Blood. Maybe they thought they were alone, but a younger camper stumbles upon them. This causes a bit of a stir among the campers, with some being happy for them and others thinking they were being inappropriate. Percy and Annabeth then have to deal with the fallout, like facing the camp counselors.
Scorpius might be more reserved and try to assess the situation first. He might not say much at first, while Rose is blurting out excuses. Then he could step in to support her explanations or add his own when he figures out the best way to handle it.
They usually react with shock and horror at first. After all, they've spent their lives denying the existence of magic. But as the situation unfolds, some might show a glimmer of curiosity, while others remain stubbornly resistant.
They might be a bit in awe at first. She has a certain presence about her that comes from her being a demigod. Maybe they're curious about her and ask Percy a lot of questions about her later.
Some characters might find it cute. For instance, Grover could just smile to himself seeing how close his friends are. He might even be a bit envious of their relationship.
Some of Percy's classmates might be in awe of Annabeth. She's smart and confident, so they could be a bit intimidated at first. But then they start to admire her for her knowledge.
She might be grateful. After all, if she has a fear or aversion to spiders, Percy getting rid of it is a kind gesture.
He may become angry. Percy has a bit of a temper, so he could lash out at the situation or even at Annabeth if she's still around. He might feel betrayed and start to question all the things they've been through together. He could also go into a state of depression. Losing Annabeth, who has been such an important part of his life, could make him withdraw from his friends and activities. He may lose his motivation for quests and just mope around, feeling sorry for himself.