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.
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.
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.
It could potentially strain the relationship. If Sirius misinterprets the situation, it might create some tension. Harry and Hermione would feel like they need to explain themselves, and Sirius might be a bit standoffish until he gets the real story. For instance, if he thought they were hiding something from him, it could make things a bit rocky between them for a while.
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.
Well, depending on the context of the fanfiction, Sirius could also be very understanding. If he knew that Harry and Hermione were just having a private conversation about important matters like their fight against Voldemort or schoolwork, he might just give them a knowing smile and say something like 'Carry on, then. Just making sure everything's all right.' He's a rather perceptive character, after all. And he trusts Harry a great deal, so he would likely give them the benefit of the doubt before assuming anything untoward.
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.
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 good 'Hermione Catches Harry and Ginny' fanfiction could be 'The Unexpected Encounter'. In it, Hermione stumbles upon Harry and Ginny sharing a private moment in the Hogwarts gardens. It beautifully captures the shock and confusion on Hermione's face. Another might be 'Caught in the Act', which delves deeper into Hermione's feelings of betrayal and how it affects their friendship triangle.
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.