One possible reason could be that Sasuke is often brooding and focused on his revenge. Sakura's more open and sometimes pushy affection might seem annoying to him as he has no room for such distractions in his dark mindset.
Sakura could initially be shocked and then try to change herself. She might think that if she becomes more like what Sasuke wants, he won't find her annoying anymore. So she could start to be more reserved and less pushy in her interactions with him.
In some fanfictions, there are scenes where Sakura is in danger and Sasuke realizes just how much she means to him. For example, if Sakura is injured while protecting Sasuke, Sasuke's reaction of guilt and his newfound determination to always be by her side can be an extremely emotional part of the story.
The relationship often becomes more strained. Sasuke's punishment can make Sakura feel resentful at first. But over time, it can also lead to her becoming more independent as she tries to prove herself to him.
She could also try to find Sasuke and clear up any misunderstandings. Sakura is not one to give up easily, especially when it comes to someone she loves. She might set out on a journey to find him, believing that she can bring him back and make him realize the importance of their family.
Sakura would probably be initially very angry. She has strong feelings for Sasuke, but kidnapping is a very extreme act. So she would likely fight back, using her medical ninjutsu skills and combat abilities to try and escape.
The dynamic would be turned upside down. Sasuke would likely become more of an outcast or a loner, feeling rejected. Naruto would be in a difficult position, having to balance his friendship with Sasuke and his new relationship with Sakura. Sakura would be the catalyst for this change, and she would have to face the consequences of her actions, like dealing with the villagers' opinions and the potential backlash from Sasuke's supporters.
A fanfiction could involve a situation where both Sakura and Sasuke are dealing with jealousy in different ways. Sakura is jealous of the attention Sasuke gives to his ninja goals, while Sasuke is jealous of the friendships Sakura has with other guys. This creates a lot of tension and drama between them.
One popular type of fanfiction could be about their friendship. For example, a story might focus on a mission where Sasuke, Sakura and Naruto have to work together in a really difficult situation. They could use their individual skills, Naruto's brute strength and positive attitude, Sasuke's cool-headedness and powerful jutsu, and Sakura's medical knowledge and combat skills to overcome the odds.
I would recommend 'The Road to Redemption'. In this fanfiction, Sasuke has to face the consequences of his past actions and Sakura is there to support him. It delves deep into their complex relationship and how they grow together. It also has some exciting action scenes that add to the overall story.