What are the central characteristics of “Sonny’s Blues” by James Baldwin that, in your view, contribute to a successful or satisfying story?

Let's turn this question around. Words like "successful" and "satisfying" aren't very useful in questions like this one, because they suggest that you have to actually like the story—which you may not. If you didn't particularly enjoy a story, it can be hard to think of anything "successful" or "satisfying" about it. But whether or not we enjoyed a story, we can consider what makes it successful in terms of achieving its goals or fulfilling its purpose. So, what are the goals and purpose of this story, and how does Baldwin achieve them?
Like most of Baldwin's writing, this piece focuses on the difficulties and challenges facing the black community in America. As such, there are various characteristics of this story which help us understand the points he is making. First of all, the first-person narrator helps create a sense of intimacy between the speaker and the reader. We feel sympathy for this man who is talking directly to us, a man who "taught my classes algebra" and worries for the boys in his class who might one day end up where Sonny is. The narrator has succeeded in becoming a responsible member of the community, and the reader consequently respects him for that, but Baldwin uses this intimacy fostered between reader and speaker to emphasize that this is almost a matter of luck. Because black boys grow up in a community where drugs like "horse" were available to them at school age, and in projects where they were forgotten by the government, the difference between becoming an algebra teacher and becoming a drug addict can be a matter of chance. The realism of the story, and the nature of the first person narrative, helps us better understand the "darkness of [black children's] lives."
The writer of the story is conversational, his language erudite but utilizing language features (sentences beginning with "and" and "some," for example) which help us to imagine that he is telling his story only to us. As such, we are drawn into his internal conflict and emotional journey as he thinks about his brother. The effect of this is that, when the narrator's mother tells him the story of what happened to his uncle, we are as shocked as he is, and we feel the resonance of the line: "till the day he died, he weren't sure but that every white man he saw was the man that killed his brother." Along with this, the reader suddenly recognizes the many unspoken sides to these Harlem stories and just how fraught Sonny's existence necessarily has been.
As such, at the end of the story, we too have come to want to give Sonny a second chance. Notably the "darkness" at the story, which once symbolized menace and threat, has come to mean something else in the "darkness" of this club, where "coal-black" jazz players welcome the brothers in. Here, they are among their people in their "dark corner," the language echoing the narrator's own reinterpretation of blackness—and of Sonny's musical gift. Here, Sonny is in his element, and his music becomes a "triumph" of its own.