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 grabs my hat could be a simple yet interesting story. Maybe she grabs it because she wants to play a joke on me. She might put it on her head and make a funny face, and we end up laughing.
Well, it could be a story about a girl who suddenly grabs someone's book. Maybe she's in a hurry and mistakes it for her own. It might lead to an interesting encounter, like an apology and then a new friendship starting from that little incident.
One common theme is the exploration of their relationship. Given their different personalities in the original work, fanfictions often focus on how they bridge the gap between them, like how Giyuu's stoicism and Shinobu's more cheerful yet calculating nature interact.
One possible plot idea could be the exploration of how Mitsuri and Obanai deal with the impending arrival of their baby. Maybe they face challenges like preparing a safe home in their demon - slayer world. Another could be the reactions of their friends and comrades to the news.