The sister was probably in shock at first. Finding out that her brother killed their mother would be an extremely traumatic event. She might have been frozen in disbelief for a while.
She could be very sad. After all, Naruto is likely an important person in her life. She might feel abandoned and start to question why Naruto left her.
In a Giyuu x Shinobu fanfic, the setting and plot can vary widely. Some might be set during the main events of the Demon Slayer universe, with them facing demons together. Others could be more of an alternate universe story, where they meet under different circumstances, like in a modern - day high school AU. The fanfic could also delve into their backstories and how those experiences shape their relationship. For instance, Shinobu's past with her sister could play a role in how she opens up to Giyuu, and vice versa for Giyuu's own traumas.
I would recommend 'Whispers of the Heart' for Giyuu x Shinobu fans. This fanfic focuses on their unspoken understanding. It's full of small moments that build up their relationship, like when Shinobu leaves a small flower on Giyuu's doorstep as a sign of her care. Also, 'Shadows and Sunlight' is worth checking out. It has a great plot that involves them having to go on a secret mission together and how that journey changes their relationship from colleagues to something more intimate.
She might feel guilty. Since they are siblings, she could be aware of Naruto's neglect and try to make it up to him in small ways, like sharing her food or secretly leaving him little gifts.