That movie was based on the Haruki Murakami short story “Barn Burning,” though it did reference Gatsby directly in the dialogue

Yes it did mention the Gatsby. The author was obviously interpreting the psycho-thriller angle by design.

The privileged versus unprivileged; being trapped and unable to achieve the dream and living with unfulfilled desires...

I watched Burning and Parasite as a duology, both have very similar themes about modern day Korea. I'd suggest you watch them back to back as well.

Great minds think alike! I have seen the Parasite too but few months before the other one.

The Parasite has won an Oscar I think.