Sakura could develop by becoming more independent. In an Akatsuki - centered fanfiction, she'd be out of her comfort zone in Konoha. So, she'd have to rely on her own skills and judgment more. For example, she might learn new jutsu or combat techniques from the Akatsuki members she's with.
Well, a plot could involve Sakura being kidnapped by the Akatsuki. Instead of being a damsel in distress, she starts to understand their motives and gradually changes their views on Konoha. Or perhaps there's a story where Sakura is on a mission and accidentally runs into the Akatsuki. She then has to use her wits and combat skills to either escape or form an uneasy alliance with them.
Sakura would likely be in a position of constantly challenging the Akatsuki. She has a strong sense of right and wrong. However, some Akatsuki members might respect her for her tenacity. For example, Kisame might find her spunk entertaining. At the same time, Sakura would be trying to figure out how to deal with each member's unique abilities and personalities. Deidara, with his explosive art, would be a particular challenge for her as she tries to avoid getting blown up while also trying to understand his motives for being in the Akatsuki.
One idea could be Sakura getting caught in the middle of an Akatsuki mission. She might try to use her medical skills to help some of the Akatsuki members who are injured, leading to a strange alliance. Another could be Sakura being sent to spy on the Akatsuki, but she starts to question her own village's motives as she gets to know them better.
If Sakura Haruno joins Akatsuki in fanfiction, her character could experience a significant shift. She might start to question her previous beliefs. Akatsuki is known for its anti - village ideology in some ways. Sakura, who has always been loyal to Konoha, would be in a moral dilemma. This could lead to her developing a more complex personality as she tries to balance her old values with the new ones she encounters in Akatsuki.
With Naruto, it would be a huge shift. Naruto has always seen Sakura as a friend from Konoha. If she joins Akatsuki, Naruto would be confused and probably try to convince her to come back. Their relationship would become strained as they would be on opposite sides, at least initially. Naruto might see her as a lost friend that he needs to save.
There could be the patients, of course. Each patient might have their own unique backstory and personality. Maybe there's a young patient who is dealing with trauma, and Sakura has to find a way to reach out to them.
I'm not sure if there is a specific 'sakura haruno seduce fanfic' readily available. You could try searching on fanfic platforms like FanFiction.net or Archive of Our Own, but keep in mind that the content should be appropriate and in line with the platform's rules.
One great 'sakura haruno fanfiction' is 'A New Beginning for Sakura'. It shows Sakura in a different light, with her exploring new jutsu and relationships outside of the main Naruto storyline.
I'm not sure specifically as there could be many different versions of this fanfiction. It might involve Sakura having some sort of relationship or adventure within the Akatsuki group. Maybe she could be a spy among them, or perhaps she gets involved in their various missions and power struggles in a unique way.