Hermione isn’t human and her friends don’t care.
Basically, Hermione isn’t human. She never had been. For all her smarts, she doesn’t quite remember how she came into the world as a daughter of two human dentists. Still, her parents were nice, but interacting with other humans her “age” was boring, which is why she turned to literature.
Then she was taken to Hogwarts after being discovered as a “witch.” By technicality, she was, but she was a little miffed that her powers were limited to just “magic.” Anyways, she went to this magic school. Despite her vast knowledge of the universe, her memories that transcended time, she was still a child in human flesh, so her emotions still affected her unlike other entities.
She still felt excitement from seeing the floating candles. She still felt happiness from being sorted. She still felt annoyed her classmates don’t follow the rules (her existence doesn’t follow the rules as well but still!). She still felt hurt when her peers called her bossy and made fun for having no friends.
And then she felt something weird when two boys burst into the restroom just when Hermione was about to deal with the Troll. It was really under control, but she was at least grateful for the interruption; it would’ve been a pain if she was figured out so soon.
She ended up friends with Harry and Ron. They felt… familiar. She think she knew them. Maybe in a different life? A different timeline perhaps? Whatever the case, she has a fondness for these friends of hers.
Yep. She’s going to have fun in this life with these two. She just has to make sure that she hides her true nature. She doesn’t want a repeat of what happened last time (she still shivered when she remembered accidentally blinding a few hundred people).
Time to be a totally human normal witch!
Meanwhile, Ron can instantly tell that something is off with Hermione. He doesn’t know why, but something about this girl made the hair on his neck stand up and the back of his eyes fuzzy. Still, she’s… nice, he guess. He guessed that she’s not a bossy know-and-all. She’s kind of cool (don’t tell her that!). Ron would let it go, just this once.
With Harry, he doesn’t notice any weirdness. Well, he does, but having his world turned upside down in a matter of months really forced him to be adaptable. He thinks Hermione is nice, albeit a little weird. But hey, they’re wizards and witches; everyone’s weird! He’s just happy that he got not one, but two new friends to hang out with! :D