i think the 'percy is clueless about annabeth's feelings from him/his feelings for annabeth' thing technically comes from botl. and i will acknowledge there's like three things that give this impression: he's telling his mom it's not a date in the beginning of the book, he tells rachel he doesn't know what annabeth's problem is and rachel alludes to him being totally blind, and he says his mom seemed to understand what was going on between him and annabeth but that he himself did not.
but none of these three things necessarily suggest that percy is not aware of the romantic subtext between them - and the book before this and after this makes that reading impossible, actually.
it's fair to say he's being clueless about how to handle the situation or fix the situation now that it's grown so complicated and messy and painful. and in this regard, i feel it's worthwhile to mention that annabeth is equally as lost and clueless as he is.
when it comes to "it's not a date mom oh my gosh" i think it's quite obvious that the very fact that she's teasing him about it and he's embarrassed about it means he knows that it is a date, he's just got to be a moody teenager about it. and also serves to indicate that while the milestone is significant, percy and annabeth are not yet ready to call it like it is. it's age-appropriate immaturity. worth pointing out that neither one of them has been on a date ever, because they're fourteen years old.
when it comes to rachel - he was initially slow to understand annabeth's fury in the first few chapters as jealousy, sure. but i think it's just because, from his perspective, it's totally irrational - he says and does all the right things ('i never thought about [whether she was pretty or not]' 'seriously, i barely know her'), and none of it matters to annabeth and she won't even hear him out. and then she happens to mention she'd visited camp a few times during the school year and he is hurt she never told him she was in town (fairly, i would say - she seems to be intentionally initiating distance between because she's also hiding that luke came to visit her that year!)
but later in the book, chiron told percy to his face point blank that annabeth was jealous of rachel, and percy's literal verbatim response was "that's stupid." kid you not. like i suppose if you want to accuse him of being clueless about how to handle a jealous girl, then go for it, but again. it's not as simple as obliviousness - it's more like 'she has no right to be acting this way and i didn't do anything wrong so i refuse to be the one to humble myself. she's being unreasonable.' and to a certain extent she is - there is literally no romantic element to percy and rachel's relationship at all at this point, and bringing rachel on the quest is the right answer, confirmed by two olympians and chiron. so annabeth's bitterness toward percy and lashing out at him is projection of her own insecurities. in other words, she's being unfair to him. this is not a knock on annabeth because i think anyone (guy, girl, young, old - anyone) in these specific circumstances would be down bad, particularly after she just made herself so vulnerable by kissing percy and then bawling her eyes out grieving for him. it makes all the sense in the world that her feelings are hurt and she's embarrassed. i think percy's greatest fumble is just not manning up and reassuring her, but again, you really can't be too hard on him, since he is quite literally just a kid - ppl a lot older than fourteen would not be quite sure on how to handle it if their best friend kissed them & then their reunion ended in her storming out and refusing to speak to him lol. of course the right thing to do would be to just talk it out. but that would require confessing their feelings with words. and they're both immature and not ready for that. so the situation escalates. percy seems to be playing dumb to rachel when he says he doesn't know why annabeth is being so mean to her - again, chiron already told him to his face that she was jealous. i think what percy's really expressing is that he's sorry annabeth is being so unfair towards rachel, and being unwilling to admit that he could at least help the situation by just talking to her.
but no, percy's not clueless that annabeth is jealous of rachel - it's why he doesn't tell annabeth when they're hanging out, why he's awkward saying goodbye to rachel at the end of botl. when he finally does bring up rachel to annabeth in tlo he admits he's 'asking for trouble.' beckendorf literally is teasing percy about not mentioning rachel kissing him to annabeth, and percy is like 'you better not.' he absolutely knows. he just doesn't think she has a right to be so petty about it when they're not dating - which is why, in the first few chapters of tlo, he's like 'i felt guilty for hanging out with rachel. then i felt angry that i felt guilty. i was allowed to have friends, right?"
percy is totally upfront with us that he thought they'd 'get through the strangle-each-other phase' in the beginning of tlo. he's also totally aware that annabeth is making a move when she brings up 'people who are important' during the cabin inspection. but the reason that they're not dating, in percy's mind, is because annabeth is in love with luke and refuses to talk to percy about luke for an entire year. he tries to talk to her about luke numerous times the summer of the labyrinth, she freezes him out, then she tells him her prophecy and he (naturally) assumes she's actively in love with luke. annabeth tries to explain but isn't able to before they get interrupted. then percy tries to tell annabeth that he doesn't want to be distant from her, he gets interrupted, annabeth uses it as a cue to escape the conversation and runs away from him and doesn't look back once.
i think the only genuine example of cluelessness is annabeth not realizing percy is jealous of luke - he barely expresses it, in her defense, except for this moment on olympus:
She shook her head in disbelief. "Do you have any idea how dangerous that was?" "I had no choice," I said. "It's the only way I can stand up to Luke." "You mean . . . di immortales, of course! That's why Luke didn't die. He went to the Styx and . . . Oh no, Luke. What were you thinking?" "So now you're worried about Luke again," I grumbled. She stared at me like I'd just dropped from space. "What?" "Forget it," I muttered.
like i'm telling you, before this moment, she didn't know, lol.
anyways. by about the midpoint of tlo i think they've both become so emotional and scared of losing each other that it kind of forces them to humble themselves and be vulnerable - percy admits to feeling 'like a jerk' and wanting to explain to annabeth that he didn't ask rachel to come in the helicopter (it's not his fault but like he doesn't care about that anymore, he just wants to make her feel better). annabeth tells percy that luke came to visit her. percy admits to annabeth that he just doesn't want luke to hurt her anymore, and she tries not to get angry.
like! there's no other way to read this but teenagers being petty to each other and too insecure to be vulnerable about their feelings, then rapidly maturing because they're confronted with the much worse alternative - losing the other person.
