It certainly looks like Harry is a horcrux in this universe, and Harry already thought of that possibility in different terms, yet the Sorting Hat says with 100% confidence that there is no extra “mind, intelligence, memory, personality, or feelings” in Harry’s head.
I would add that in Cannon, Harry is a horcrux, which adds a fair amount of weight to the idea.
Some possibilities for why the hat would make the statement;
Harry’s scar isn’t a horcrux.
A horcrux is nothing like a ghost, mind, intelligence, memory, personality, or feelings.
The sorting hat was wrong, or lying.
Something about Harry-the-horcrux prevents detection by sorting hats. For example, it can’t be active (and therefore the hat can’t detect it) unless Harry is in dark side mode.
Something about Volemort’s horcrux is different than the hat expects. For example, an occlumens can hide from detection.
While I like the idea that the horcrux is only active when Harry is in dark-side mode, I can’t see any reason to favor that theory.
I would add that in Cannon, Harry is a horcrux, which adds a fair amount of weight to the idea.
Some possibilities for why the hat would make the statement;
Harry’s scar isn’t a horcrux.
A horcrux is nothing like a ghost, mind, intelligence, memory, personality, or feelings.
The sorting hat was wrong, or lying.
Something about Harry-the-horcrux prevents detection by sorting hats. For example, it can’t be active (and therefore the hat can’t detect it) unless Harry is in dark side mode.
Something about Volemort’s horcrux is different than the hat expects. For example, an occlumens can hide from detection.
While I like the idea that the horcrux is only active when Harry is in dark-side mode, I can’t see any reason to favor that theory.