First and foremost, Rosamund Pike is Mother.
Secondly, I'd like to talk about Harry Potter in Saltburn. Allow me to preface this by confirming that JKR is an absolute shithead and can sit on a hot poker.
So throughout the summer, we see Felix, Venetia and Farleigh passing around a copy of the final Harry Potter book. It makes a huge amount of sense for them to read it! They're all in that strange stage of arrested development one forms at uni, because you're an adult living independently for most of the year, but then you come back to your parents' house and return to a teenage state. Surrounded by physical reminders of your childhood, you may well regress and re-engage with old media. I think many people have returned home and listened to CDs or flicked through forgotten video games. So there's a sense of nostalgia.
It also helps to ground Saltburn in the mid '00s. The hiddeous fashions are hilarious, the phones are bricks, and everyone was reading Harry Potter and the Deathly Hallows, the final installation in the saga. Given that Felix, Venetia and Farleigh are in their late teens/early 20s, it would make sense for them to have grown up reading those books. Again, I can't be the only person to interact with media I've "aged out" of because, well, I've invested so much in the series. I imagine a fair number of people who read the final book(s) weren't officially part of the target audience, but read it because they felt nostalgic or curious about how the story ended.
Finally, there are some obvious comparisons between Harry Potter and Saltburn. Both take place primarily in a beautiful old building and feature a character (Harry and Oliver) who wants to join a different world (magical/extreme wealth and status). You could also compare the characters of James Potter and Severus Snape with Felix and Oliver. You have the popular, desirable person, and then the jealous, slimy genius. There are classical allusions in Harry Potter and JKR actually read classics and French at Exeter uni. The joke about Cerberus, guardian of the underworld and terror of 11 year olds being named "Fluffy" is pretty hilarious. Farleigh reads English at Oxford, so he's going to get those references... even if he's not especially literate or into books.
Oliver, of course, doesn't read Harry Potter. It's too pedestrian and reminds him of the life he's trying to leave behind by cutting ties with his parents. Oliver is a total snob, and wouldn't deign to interact with anything like that. I don't really think Oliver even likes reading, to be honest. Do we ever see him with a book? He does it before uni and completes the reading list, yet when he mentions this to the professor, the professor is shocked. Then he ignores Oliver. Oliver only does things which he thinks will benefit him, other than when his sensory, animalistic, sexual desires finally come through. See - fucking the graves.
Anyway, you should watch Saltburn. It's excellent! Beautiful! The cast is gorgeous and talented! Everyone is psychotic!