Well, Sirius is a very protective character. When he discovers that Harry is a Horcrux in the fanfic, he could initially be in denial. But once he accepts it, he'd likely start looking for ways to either protect Harry from Voldemort or find a way to remove the Horcrux part from Harry. He might also feel angry that Harry has been put in such a dangerous situation.
In this fanfic scenario, Sirius' reaction would be complex. He has a strong bond with Harry. Learning about Harry being a Horcrux would shatter his understanding of Harry's situation. He might first feel a sense of helplessness, realizing that the danger Harry is in is far greater than he thought. Then, he would probably try to consult with other wizards or witches he trusts, like Lupin. He'd be desperate to find a solution to keep Harry safe while also dealing with the implications of Harry being a Horcrux, such as how it affects Harry's soul and future.
Sirius might be shocked. He'd probably feel a mix of horror and protectiveness. He'd be horrified that Voldemort has used Harry in such a way and would be even more determined to keep Harry safe from Voldemort's clutches.
One possible consequence is that Harry becomes an even bigger target for Voldemort. Since a Horcrux is important to Voldemort's immortality, he'd be more determined to get to Harry. Also, Harry might start to experience some strange effects on his soul or magic due to being a Horcrux.
One implication is that Harry's life is in even more danger. Voldemort might be more determined to keep him alive until he can fully use Harry for his own evil purposes.
Sirius would probably be shocked at first. Then, he'd likely feel a deep sense of sadness and guilt. He might think that he should have been there more to protect Harry from getting those scars.
Harry may also feel a sense of adventure. Despite the situation, he's used to facing strange and dangerous things. He might start to think about how he can use this situation to his advantage, like finding out more about his parents or the secrets of the wizarding world that Sirius might know. He could be a bit excited as well as scared. For example, he might be thinking that this could be a chance to get away from the Dursleys for good.
The relationship could also take a more complex turn. Other characters might get involved in their conflict. Some might side with Sirius, thinking Harry was in the wrong, while others might try to mediate. This outside influence could either help or hinder the mending of their relationship, depending on how it's handled in the fanfic.
At first, Harry might be extremely confused. He trusts Sirius to a certain extent, but being kidnapped is still a shock. He would probably ask Sirius a lot of questions like 'Why are you doing this?' and 'Where are we going?'
Sirius might immediately rush to Harry and give him a big hug. He's like a father figure to Harry, so physical comfort would be his first instinct.
Snape might be secretly pleased at first, seeing as he has no love for Sirius. But then, being a teacher, he'd probably feel obliged to report it. He also might use this situation to his advantage against Sirius in the wizarding politics within Hogwarts.
He might be initially embarrassed, especially if he receives it in a public place like the Great Hall.