What makes "Paul's Case" a modern story?
One of the key features of Modernism as a literary movement is a massive focus on the thoughts and feelings of central characters and how they are expressed. This became known as the stream-of-consciousness, and is most famous in the works of authors like Woolf and Joyce, who followed the free thought of their characters, which is often illogical and moves from one association to another. This however, is something that we can see in Cather's description of the thoughts of Paul in developing a fully psychologically developed character. Note how she does this when he realises his jaunt in New York is up:
It was to be worse than jail, even; the tepid waters of Cordelia Street were to close over him finally and forever. The grey montony stretched before him in hopeless, unrelieved years; Sabbath school, Young People's Meeting, the yellow-papered room, the damp dish-towels; it all rushed back upon him with a sickening vividness.
The stream-of-consciousness narration is therefore used to show Paul's internal feelings and the string of associations that he has with failure and home, which reinforce to the reader the price of failure for Paul and how impossible it is for him to return home. This is a key modern aspect of this text, as the narration shows Paul in his full psychological complexity.