He might meet the future versions of Naruto and Sakura. Their relationship with him could be very different in the future, perhaps they are now leaders of the village and Sasuke has to adjust to their new status.
Sasuke could also be motivated by power. He might believe that Sakura has some sort of knowledge or power that he needs. By kidnapping her, he can force her to give it to him or help him obtain it. This could be related to her medical skills or some hidden power within her that Sasuke has discovered.
Since 'hard lemon' fanfiction is inappropriate, we can talk about their general characteristics in normal fanfiction. Sasuke is often depicted as a brooding and powerful character, while Sakura is shown as strong - willed and loving. In non - inappropriate fanfiction, their relationship might be shown as evolving from initial acquaintance to deep love, with Sasuke's cold exterior gradually melting due to Sakura's unwavering affection.
Sasuke would likely be aloof and guarded at first. He might see Batman as just another 'vigilante' like some of the shinobi in his world. Batman, on the other hand, would be cautious and try to figure out Sasuke's motives. Eventually, they could start sharing their combat techniques. Sasuke might show Batman how to use chakra in combat, and Batman could teach Sasuke about the importance of having a strong moral code.
I think young Sasuke would have a very intense reaction. He was so consumed by his hatred for Itachi at that young age. A Sasuke vs Itachi fanfiction would be like a trigger for him. He would be eager to see how the fictional fight is portrayed. If Sasuke in the fanfiction is shown as strong, it might fuel his own ego and make him strive even harder to become powerful. However, if the fanfiction shows Itachi as superior, it could enrage him. He might feel that it undermines his own goal of defeating Itachi and he might even want to find the writer to correct their 'wrong' view.
One common theme is Sasuke's struggle to admit his feelings. When he's jealous, it shows that he actually cares more about Sakura than he lets on. Another theme could be misunderstandings. He might misinterpret Sakura's interactions with others as something more than friendship.
He might focus on rebuilding relationships. After the war, Sasuke could be trying to mend his bonds with Naruto and the others in the fanfiction. He may also be involved in restoring his clan's honor in a more peaceful way.
It might be for Naruto's own good. Sasuke may believe that Naruto is on a dangerous path that will lead to his downfall. So he captures him to keep him from making bad decisions, like sacrificing himself for the village or something similar. He wants to save Naruto from himself in a sense.
In some fanfictions, Naruto might reject Sasuke because of Sasuke's continuous pursuit of power in a way that endangers others. Naruto, who values friendship and the safety of the village, could see this as a betrayal of their shared values.