Sirius Black is a responsible adult.
Lately I've come across different opinions regarding Sirius in his manifestations in relation to other people, so I decided to return to the books and provide my perspective on this situation.
When we think of Sirius, we most often imagine a highly impulsive person, chasing thrills, "indulging his instincts" (as Severus put it). However, it would be foolish to reduce everything to such a superficial image.
“It is better to die than to betray friends.“
Immediately after the tragedy, Sirius rushed to Godric's Hollow and insisted that his godson stay with him. However, Hagrid, obeying Dumbledore's orders, announced that Harry would be living with the Dursleys. Sirius, though hesitantly, agreed, even offering his motorcycle so Hagrid could get the child home more quickly.
After this, Black goes after Peter. Many interpret this as revenge. But the truth is different: he knew Pettigrew was the secret keeper, and as long as he lived, Harry was in danger. He wanted to track down and eliminate Peter without trial. This, of course, was partly out of anger and revenge, but mostly an attempt to keep Harry safe.
”He would come to live with me.”
Upon learning of the conditions his godson was living in with the Dursleys, he, on the run and still branded a murderer, was completely out of his depth. He even offered Harry to live with him (which ultimately didn't happen), but here's what Potter says about him next:
"...He was convicted of murder, but he escaped from a wizarding prison and is now in hiding. But he keeps in touch with me... He worries about me... He makes sure I'm well..."
The most important moment, in my opinion, occurs in "The Goblet of Fire." After receiving a letter from his godson detailing everything that happened, Sirius doesn't simply respond with a written reply. Still a wanted criminal, he takes on the guise of Padfoot and spends two weeks in Hogsmeade, feeding on dead rats and living on the streets. Any mistake threatens to send him back to Azkaban, but he stays put because Harry needs someone nearby, someone who can offer advice and help.
At the Ministry of Magic, Sirius once again displays the same impulsiveness that many question his "adulthood." But in this episode, it's important to consider the context. He rushes to Harry's aid because, unlike many other adult characters we've seen, he's not prepared to put the interests of the Order above a child's life. He risks himself first and foremost for his godson, not for the Order's goals.
What's the result? Sirius would never have been the ideal parent (not only in everyday life, but in general). Life robbed him of the opportunity to be a "normal" adult. However, he becomes a model of devotion and responsibility. He is able to channel his emotions and thereby protect his loved ones, and he is willing to sacrifice everything.
As Dumbledore noted in a conversation with Harry, Sirius was to him what James was to Sirius himself: "the closest friend" and, I would add, the most responsible adult who simply did not have time to live in the normal world.