I honestly think that Snape would be more likable if Harry was not the narrator. That's what's bad about writing in first person, you only see things throught the eyes of the character, with all his bias. Let's be real, Harry was blinded with hatred and may have painted Snape worse than he actually was. if it was third person, we would see things from another perspective
first off to clear this up - hp is actually told from third person (he/she/it) but it’s what we call limited or close third person, in that it only follows the thoughts and feelings of one character (in hp’s case, very close since we are literally immersed in harry’s feelings). the opposite of this would be omniscient third person, which can jump to a variety of characters or stay at a removed distance from all the characters and develop a distinct narrator’s voice that way. first person is when a character uses ‘i’ and it’s usually close (we only follow the one character) so i can get why you’d get them mixed up - they’re very similar.
but as to your point - absolutely harry colors our perception of snape. harry is an unreliable narrator, something rowling uses to her advantage several times throughout the novel for dramatic effect. he doesn’t know everything and the incomplete judgements he makes based on his partial knowledge aren’t always correct. he has his own biases and preconceptions and that colors the way he not only reacts to characters, but how he interprets them.
for example: harry thinks snape seems disappointed that he doesn’t get to poison neville’s toad. but snape doesn’t tell harry that and harry is basing his interpretation on his reading of snape’s facial expression - so snape may or may not actually feel disappointed. we can’t know for sure bc we’re viewing snape through harry’s lens and harry isn’t infallible or objective.
i’ve said this before, but characters who aren’t pov characters are really only autonomous through dialogue - that’s when they are speaking for themselves. obviously that can be tricky - take snape, who literally cannot say what he’s thinking a lot of the time due to his spying work - but pretending that harry’s interpretation of snape’s facial expression or what harry thinks snape is feeling is somehow rock hard evidence for who snape is as a person is ridiculous. harry can’t know and we can’t know unless snape tells us.