There is a fanfiction titled 'Under Sirius' Watch'. In it, Sirius catches Harry and Draco sneaking around the castle at night. This leads to a series of events where Sirius has to decide whether to report them or try to understand what's really going on between the two. The story delves deep into the characters' emotions and the complex relationships within the Hogwarts world.
There are also fanfictions where Sirius catches them and instead of being angry, he is curious. Like in 'Sirius' Curiosity', he decides to observe them secretly for a while to figure out what their relationship really is, rather than jumping to any hasty judgments.
One common theme is the theme of mentorship. Sirius often takes on a mentorship role when he catches them. He uses his knowledge of the wizarding world, especially the darker aspects, to guide Harry and Hermione. Another theme is friendship. Their friendship is tested and strengthened when Sirius catches them in some kind of 'forbidden' activity. It shows how they support each other through difficult situations.
One possibility is that Sirius could be initially shocked. But then, being the understanding person he is, he might give them his blessing. After all, he has seen how Harry has grown and Ginny is a great girl.
Perhaps Snape would force them to work together on a task as punishment. This could be something like cleaning the Potions classroom without magic or helping in the Forbidden Forest. During this time, they might start to understand each other better. Harry could see that Draco isn't just a spoiled brat all the time, and Draco could see that Harry has more depth than he initially thought.
Well, in that situation, Sirius would be shocked and heartbroken. He might first scold Harry for doing something so dangerous to himself. Then, being the impulsive person he can be, Sirius would probably take Harry to see someone he trusts, like Dumbledore or Madam Pomfrey. He would not let Harry out of his sight until he was sure Harry was okay and not likely to do it again.
One possible plot idea could be that Sirius catches Harry and Hermione in the middle of a secret plan to save a fellow student from a dark magic threat. Sirius, initially thinking they're up to something dangerous, then realizes their noble intentions and decides to help them. Another idea is that Sirius catches them while they are exploring a hidden part of Hogwarts that is related to an old mystery about his family. He then shares his knowledge about it with them, leading to an exciting adventure.
Snape might also keep what he saw to himself at first. Instead of immediately confronting them, he could choose to observe them further. He might be curious about what they were really up to and use his skills as a spy to find out more. This way, he could gather more information before deciding on the best course of action, whether it be punishment or something else entirely.
Sirius would be deeply affected. He'd see Harry as a sort of surrogate family, and seeing Harry in such a state would make him feel like he failed in protecting him. He'd do everything he could to make Harry feel better, from getting him medical help to just sitting and talking with him for hours about what's wrong.
Sirius might confiscate whatever Harry was smoking. He would then sit Harry down and have a serious conversation about the importance of making good choices. He could also remind Harry of the dangerous magic substances that might be out there that are far worse than normal cigarettes and that he should stay away from any form of harmful substances.