Many different opinions have been expressed about why Nick Carraway breaks the story towards the end of Chapter III. F. Scott Fitzgerald is using the fiction that the tale is being told by one of the characters in the book. The real author's purpose seems to be mainly to remind the reader of the fiction that Nick is the narrator and that he is actually in the process of writing this story. In other words, the book is not intended to be considered a novel but a sort of memoir which is not even intended for publication. J. D. Salinger did something similar with his narrator Holden Caulfield in The Catcher in the Rye, although Holden was the major character and not a minor character like Nick. Salinger's fiction was that Holden did not even consider himself a writer and was not writing for publication or writing a novel, but he was writing a memoir of an important personal experience. Nick Carraway does not consider himself a writer either. He is a bond-salesman in Manhattan and has a busy life learning his trade through hands-on experience and reading up on pertinent subjects during much of his time away from the office. Fitzgerald, the real author, evidently felt the need to remind the reader that this is not really a novel and that Nick is just telling the truth about an important painful learning experience. The key words in the sentence quoted in the question are "what I have written so far." This is a pure fiction. Nick hasn't written anything. Fitzgerald has written everything so far, but he wants to remain invisible for his own reasons; and he wants to keep Nick visible for the same reasons. Through Nick, Fitzgerald can make all sorts of personal comments, mainly about the other characters and also about the spirit of the times. Fitzgerald would find it hard to do this himself. He would be inventing characters and then commenting on his own creations, which would be awkward even for a writer of Fitzgerald's genius. Here is a small sample of the kind of comments Nick makes:
Why they came East I don't know. They had spent a year in France for no particular reason, and then drifted here and there unrestfully wherever people played polo and were rich together.
Nick is talking about Tom and Daisy. It is hard to see how Fitzgerald could have written such commentary in the omniscient third-person voice or in any other way as effectively. Nick enriches the story with his perspective. Fitzgerald would seem like an intrusive author if he tried to do it on his own, so to speak. Holden Caulfield can do it all the time because he is writing in the first-person. But Fitzgerald needs to keep reminding the reader that this is not a novel and that Nick is not a writer but only stating facts and personal impressions. This is an effective way of enhancing the verisimilitude--making it seem that all this really happened.