Literary purists would describe this book's narrative technique as "third person limited," but the limitations are so extreme that we think it's fair to say the narration is almost written from a first-person POV.
In case it's been a minute since you reviewed your 6th grade English class notes, here's a refresher: In first-person narratives, the narrator is the main character in the story: "I ran to the door when I saw the Amazon Prime delivery Subaru carrying my new portable burrito heater."
In a typical third person limited narration, the narrator is not a character in the story; they just observe the thoughts and actions of a particular character: "She ran to the door when she saw the Amazon Prime delivery Subaru carrying her new portable burrito heater."
While Hanff Korelitz's pronoun choices fit the third person technique, Grace is the narrator of You Should Have Known for all intents and purposes. Only one major sentence in the middle of Chapter Nine (9.148) reveals something to the reader that Grace herself doesn't know. Beyond that, the reader notices what she notices, hears her musings and memories, and never even reads a description of another character without it going through Grace's opinionated filter first. Korelitz's writing style is practically a stream of Grace's consciousness with all of her random asides and unrelated thoughts.
The technique is particularly effective in this book because it simultaneously puts the reader inside Grace's mind while maintaining some distance. Grace isn't exactly the type of person who wants to get all warm and fuzzy with people, but if the narration were so removed that we couldn't hear her inner monologue, readers might find it even more difficult to care about her.