I think we need to be very careful about reading too much into the character of Paul from our own cultural viewpoint. Let us remember that this story is set in a very different historical period which had very different expectations of gender roles. Just because we might analyse the character of Paul from our cultural standpoint and consider that some of the activities he engages in might suggest he is homosexual, this gives us no proof to indicate that he might have been. The story, after all, gives us no tangible proof whatsoever that he is homosexual.
The story paints Paul as a rather dreamy teenager who lives in fantasy to escape the monotony of his mundane existence. He finds himself attracted to the arts and to theatre and music as part of this escape from reality, and his act of theft from his employer and his subsequent flight to New York and his chance to experience the life he has always dreamt of having shows that he is determined to become "exactly the kind of boy he had always wanted to be." However, this is just a temporary flight from reality, and rather than face his father and a return to his humble background, Paul kills himself. Paul is presented as a young man who is out of step with his society and incapable of accepting his humble background. He is above all a dreamer who refuses to accept reality and dies, as it says in the text, with "all his lessons unlearned."
Therefore we need to be very careful about reading too much into his character. Just because he was attracted to music and the theatre and he wasn't able to accept his background and reality does not necessarily mean he was homosexual, and we are certainly given no obvious proof from the text that would lead us to this conclusion. What is far more important is the way that he is presented as a dreamer who lives in a world of illusion and fantasy.