I think one of the most tragic aspects of Sirius' death is the loss of their chance to properly get to know each other and develop a healthy relationship.

Additionally, Sirius meets restrictions whenever he tries to do something for Harry and offer him support all throughout OotP. I think that contributes significantly to the tragedy of their relationship - Sirius has never been able to display his full potential as Harry's guardian.
Among all these adults, many of whom have known Harry for several years and should know that the boy keeps getting in trouble simply because he tries to find out things he's not told, Sirius is the only one who wants to inform Harry about what's going on. He acts against Dumbledore's orders (Dumbledore, who has used Harry's curiosity since the events in PS), has to fight Molly's objections and her outright cruel accusation regarding Azkaban, and is cut short by Lupin, who never volunteers any information unless he's got his back to the wall. (Even though Lupin should have know better after so many things have gone wrong in the past because he chose to not give any information.)

So there's Sirius, trapped in this house he hates and dealing with psychological and emotional trauma and severe depression, and still he focuses on offering Harry advice as well as he can. It might be arguable whether DA was a good idea, but at least Sirius took their wish seriously to want to be able to defend themselves.