Other characters could be more practical. Maybe Chiron would see it as a sign that they need some rest. He might quietly make sure they are not disturbed and that they have a blanket or something to keep them comfortable. In fanfiction, different authors might have different takes on how other characters respond based on their own understanding of the relationships within the Percy Jackson universe.
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.
There could be characters who are a bit more mischievous. Nico might tease them about it later when Annabeth wakes up. He could make some sly remarks about how cozy they looked, which would add a bit of humor to the fanfiction story.
He could be a bit surprised at first, but then a warm feeling would spread through him. He might gently stroke her hair or cover her with a jacket if she seemed cold, all while having a soft smile on his face.
One possibility is that they've had a long and tiring adventure. After facing numerous challenges, they find a moment of peace and Annabeth, exhausted, falls asleep on Percy. It could also be a sign of their deep trust in each other. In fanfiction, this might be used to show the closeness of their relationship.
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.
Chiron would be concerned. He knows how important their relationship has been for the stability of the camp and for their own growth as demigods. He would likely try to mediate and help them work through their issues, if possible. If not, he would worry about how it will impact their future quests and the overall well - being of the camp and its inhabitants.
The campers at Camp Half - Blood would be shocked. Some might take sides, especially those who are closer to either Percy or Annabeth. The Aphrodite cabin might be all up in the drama, trying to play matchmaker again to fix things. The Ares cabin might see it as a sign of weakness in Percy and try to pick on him a bit more. Overall, it would create a lot of gossip and tension around the camp.
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 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.
Maybe she had a long day of training or adventuring. She could have been mentally and physically exhausted from dealing with various challenges in their world, like fighting monsters or solving complex puzzles.