I guess ChatGTP, like most of the Internet it was trained on, hasn't actually read Sherlock Holmes and only knows about it though pop culture references.
The stories are probably in there somewhere, but they're in there once or twice, while the pop culture Sherlock is in there thousands of times. That's got to weight things. (I just asked it to produce an imaginary Shakesheare dialogue. The results were not great.)
There are a couple of original stories where Holmes is the narrator though. These are "The Adventure of the Blanched Soldier" and "The Adventure of the Lion's Mane".