Proxima Centauri revolves around a binary pair of stars, Alpha Centauri A and B. This binary pair is more of a blank slate, too busy trying to dominate the other to cultivate life.
The visuals and conversation are provided by File as a means to help Chess translate what is going on here. From the star's point of view, in the language of gravity, the conversation is much harder to understand. It boils down to "This ship is much larger then it appears, and requires more pull then you are exerting"
At the end of the day, Chess has the hots for a personification of a mass of flaming interstellar gas that was created as a user interface by her artificial intelligence companion that, itself, is merely her own mind's creation to help her mentally comprehend the organic programming her FILE uses to access the Stellar Empathy Drive. But please don't kink shame.