But since this is Disney, and Emma Watson, and magic is real, we're going to say that this is a Potter reference.
So what about that reference? Does it add anything to the scene? Well, kind of. It connects Belle to Hermione in a subtle way. They're not that different of characters when you think about it, especially in the live-action version. Belle is now an inventor who's an outcast because of her curious mind and cleverness. Hermione, similarly, is initially branded as something of a nerd by her Hogwarts classmates. That designation disappears when she joins Harry in fighting Voldemort, just as Belle stops being an outsider compared to the Beast.
We'll allow that this creates an extremely tenuous connection between the two women. Sort of ethereal and taking on the shape of the connector. You know, kind of like a Patronus. Yeah, we just went there. Consider your mind blown.