Harry is a bit of an idiot savant, with emphasis on the idiot.
He is in his own words “Kinda smart” but it is case solving, and most of that is his subconscious, which is waaay smarter than conscious Harry. This is largely improvising, with the occasional forethought thrown in However in more recent books he is thinking more ahead on everything, he may be playing more dumb now than being dumb, as with Eb, where he outmaneuvred a wizard with three centuries on him.
He is also kinda dumb though, he still, despite knowing better, shares the wisdom of his ass when he shouldn’t, and misses things like the tension between Molly and Lara and or what is wrong with Carlos which he really shouldn’t and doesn’t ask about. He annoys people sometimes just for the sheer joy of annoying them