We gotta talk unreliable narrators for a sec.
Because I'm guilty of it to, in calling Percy an unreliable narrator, when I mean it in "he is a narrator who is unreliable" vs the actual literary device of an Unreliable Narrator.
And there is a difference, and to anyone all up in arms thinking they're arguing the same damn side what's the problem here, I shall explain.
An Unreliable Narrator (using caps here for distinction), the lit device, is a narrator deliberately misleading the audience on behalf of the author to propel a mystery or perpetuate the identity the narrator believes themself to possess.
Meaning, your narrator could be a thief or detective lying by omission to the audience to keep the game of cat-and-mouse going, or a character suffering delusions of grandeur convincing their captive audience that they're amazing until the story reveals otherwise.
Sometimes the character does this knowingly--they're deliberately hiding or skewing information from the audience. Sometimes the character does this unknowingly--they have amnesia or are led to believe information (about the story or themselves) and then feed the audience that same information.
Oftentimes, it's there for humor. Narrator says or believes or insists something that is immediately contradicted by the plot or other characters. It's also there for tragedy, see the aforementioned "delusions of grandeur".
Whatever the case, the Unreliable Narrator is a deliberate and intentional and consistent literary device employed by the author to frame their story.
There is zero basis for this argument in the first five books (we'll get to the squint-and-it's-kind-of-there for HOO in a second).
There is a difference between a character who suffers self-image issues downplaying their intelligence, abilities, importance, what have you, and a true Unreliable Narrator, and that difference lies in how this lit device resolves.
Percy's "unreliability" isn't a plot thread that ever comes to fruition. UN storylines have a moment where the funhouse mirror shatters and the narrator is either forced to see themselves for who they really are, or the story itself gives up the jig. Well-written UNs are also deliberately cued-in by the story, otherwise it ends up looking like the author is pulling story threads and resolutions out of their ass.
We know they're suspect from very early on, even if we don't know the full scope of how or why.
Percy just lacks self confidence, and, presumably, his arc would have been gaining some in a healthy way. He is unreliable, in that how he sees himself appears to be inaccurate to the true unfolding of events, but these moments aren't intended to be more than face-value.
In HOO, because we have a multi-POV story... yes, I can see where the line becomes even blurrier, becuase we have Percy's telling of events occasionally directly contradicted by other characters, but again, this unreliabiltiy is not a subplot. It has no resolution.
They never have confrontations about how Percy's perception of events so severely contradicts the truth that the other Seven argue about it. It never matters.
It might, if his "ha ha my girlfriend is lowkey abusive and I love it" actually built momentum up to him realizing this is bad. Which it doesn't.
So when Percy being an Unreliable Narrator is used to excuse plot holes, yeah, no, it's baseless. His unreliabiltiy solely concerns his self-confidence and perception of his own self-worth, powers, and strength. He'll downplay how brave he was in fighting Medusa, but he doesn't boldface lie to us that he fought Medusa at all.
It does not stretch to encompass other demigods' powers or the events of various subplots.
So... we good? We know the difference now?