I think the only real meta line is when Kylo says “You have no part in this story.” That’s a bit strange. The other meta bit is the cave scene, which clearly is designed to build anticipation for the audience. For Rey, however, a face would go a long way to help her feel some connection to her parents, something to hold onto.
The rest, I think, is consistent with Rey’s abandonment issues introduced in TFA, which Kylo keeps needling her about in TLJ.
KYLO: Your parents threw you away like garbage.
REY: They didn’t!
KYLO: They did. But you can’t stop needing them. It’s your greatest weakness.
It’s not so much who they were as identity or bloodline but who they were as people. She’s jealous of Kylo Ren; not because his father was Han Solo, but because ”You had a father who loved you, he gave a damn about you.”
That Rey’s parents threw her aware like trash is horrific, an idea Rey had to have considered but couldn’t accept until Kylo forced her to:
KYLO: Do you wanna know the truth about your parents? Or have you always known? And you’ve just hidden it away. You know the truth. Say it. Say it.
REY: They were nobody.
KYLO REN: They were filthy junk traders who sold you off for drinking money.
While “They were nobody” could be interpreted as “They weren’t important”, the takeaway I always got from the scene was Rey’s utter despair at finally acknowledging that she had been abandoned, and any hope that her parents were good people who loved her was a fantasy. It’s terrifying but engaging and relatable; and it’s undone in TROS.