Sakura might show her care for Naruto in fanfiction by always being there to heal his wounds. Since she is a skilled medic - ninja, she could be depicted as dropping everything to tend to Naruto whenever he gets injured during a mission or a fight.
Another way Sakura can show she cares about Naruto in fanfiction is by getting involved in his personal life. She could be written as someone who tries to understand Naruto's past traumas, like being an orphan and ostracized as a child. By being empathetic towards him and trying to help him deal with these emotional scars, she shows that she truly cares about Naruto as a person, not just as a comrade.