Its explicitly fiction, so “real” is…perhaps not the right word. I think the story is intended to be read literally as fiction; its a fictional world where “puppeteers” that can somehow temporarily exist within you and direct your actions, and also pop out of you and leave you on your own are a real kind of personal service you can hire, and where also VR headset that let you relive past experiences are real things you can get (by the end of the story, at least.)
On the other hand, I think the puppeteer element intentionally can serve as allegory for one or more things in the real world; both gender transition and mental health care via professionals and drugs seem like they could fit, more or less. I don’t know if one thing in particular was intended, though.
But I don’t think that’s the intent of the story — I think the author did intend for this to be taken literally as a fictional tale, and it’s quite good.
Jeff disappears from his parents', sister's, and wife's life, because none of them accept Jeff + Michelle as an integrated person, someone whose anxiety and depression is unacceptable to them (unacceptable to any of them) but neither is his attempt to pull himself together and become happy and well-adjusted (acceptable to his wife, unacceptable to his parents, acceptable to his sister but only on the condition that he make amends with his parents). Danny is Jeff's true biological son, and when the narrator thinks that she sees Jeff "pulling Danny's strings," what the narrator is really claiming to understand in the end is that she isn't capable of trusting that anyone can be genuinely happy in-and-of themselves, that the projection of happiness must be a front, intended to meet roles and expectations, and not from a genuine inner source.
The story is a tragedy, but not about Jeff. It's a tragedy about the unrealistic expectations often fostered in immigrant families (including the narrator's failure to land a rich husband or build a life outside her parents' conflict management issues and control), and how these expectations can wreck family life.
But then it goes off the rails. We quickly learn Michelle is somebody entirely other, whom we learn practically nothing about despite that she authored an extremely likeable Jeff. We learn that the other, peevish, Jeff is just Jeff from before college, before he was scripted up. We also learn practically nothing about him. The only character we learn anything about is fake Jeff, and then only a variety of impressions of him.
It has elements of a good story, but omits the good parts.
Additionally, I'd say that none of them result in a fully plausible story, and that the author wrote it like that intentionally.
And I vastly prefer it that way to a pure allegory, which to me too often seems like a dishonest way to make an argument.