I don't know if this is controversial but I think the characterization of movie!Percy could be what book Percy would have become if he wasn't introduced to the demigod world at 12.
And to be clear i'm not saying that the movie was right to age him up, i'm not part of the crowd that glaze the movies just because the show also sucks (albeit in different ways). It's a thinking exercise, an au where things doesn't happen until Percy is 16.
That boy had anger issues and suicidal thoughts as a preteen, and I don't think things would have gotten better past that point. 12yo Percy was still trying on his classes, paying attention when a teacher actually made a effort to make the class interesting. Four more years of being bullied by his peers and dismissed by his teachers and he would probably stop trying and use earphones on classes as well.
12yo Percy was still only thinking his insults to Gabe, but couldn't actually say or do anything about him. Four more years and Gabe would probably be worse as Percy grew up, and he would definitely clock the abuse that Sally went through and eventually call him a bald headed freak to his face, probably escalating to a physical fight between them.
Four more years of thinking he's going insane by seeing creatures that aren't supposed to exist and feeling lonely as hell I totally see him just fleeing to the bottom of a pool to be alone and in peace, or maybe staying out late in odd jobs, skate parks, anything to avoid going home.
12yo Percy still wanted to impress his dad, earn his respect and got both a little sad and proud after his conversation with Poseidon at the end of TLT. Four more years of neglect and I see him being unimpressed and dissmissive of Poseidon and the supposed rules the gods have to follow. That could've made him so much more tempted to join Luke too. Except that Luke still fumbles and the titans are still worse, but being on the gods's side would be a struggle.
Regarding Annabeth he would probably be less annoyed by her know-it-all bossy demeanor and more determined to impress the striking Camp veteran in war games (but like. an actual older version of annabeth, not that Clarissabeth-mashup movie abomination) whether he admitted it or not. And I think the Athena vs Poseidon rivalry could be more intense and fill the rivals to friends to lovers trope.
And it all points to him being darker, more angry and more unhinged but it's very important to me that despite all he went through Percy still remains kind. He still rescues animals caught in nets in the ocean, he's still the type of guy to buy a rubber rat he doesn't need or want just because the store owner seems a little sad and pathetic, he's still taking outcasts under his wing. He looks a bit rugged and intimidating at first but that's only until he smiles at you and while he's not the best articulating his feelings he gives the best hugs that make people feel safe.
