In a 'kokushibo meets tanjiro fanfiction', one possibility is that Kokushibo senses something different about Tanjiro right away. Maybe it's the fact that Tanjiro has a unique scent or an energy that Kokushibo has never encountered before. Tanjiro, being Tanjiro, would be ready to face Kokushibo head - on, but also be open to communication if there's a chance. The story could explore their different views on the world of demons and slayers, and how they might come to understand each other better through their encounter.
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.
For Tanjiro, he could become more understanding of the complex nature of demons. Meeting Kokushibo, a powerful and complex demon, might make him realize that not all demons are simply evil. Kokushibo, on the other hand, could start to have some doubts about his loyalty to Muzan. Tanjiro's tenacity and belief in the good of all might start to chip away at Kokushibo's cold - hearted exterior.
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.
The battle of Yoriichi vs Kokushibo can be found in the advanced stages of the Demon Slayer manga. It's an intense and highly anticipated confrontation. The build-up and action are both masterfully depicted.