Tanjiro might use his sense of smell to detect hidden threats. Since his sense of smell is super - enhanced, he could sniff out any demons or traps in the way of saving Rengoku. For example, if there are demons disguised as allies, Tanjiro would be able to tell by their scent.
One possible plot twist could be that Tanjiro has to sacrifice a part of his own power to save Rengoku. Maybe he has to give up some of his newly acquired breathing techniques which he has worked so hard to master. This would show his selfless nature and his deep respect for Rengoku.
One common theme is adventure. Since both characters are from the Demon Slayer universe, they often go on demon - slaying adventures together in the fanfictions. They might face powerful demons and rely on each other's skills to survive.
You can try fanfiction platforms like Archive of Our Own (AO3). There are a large number of fan-created works there. Just use the search function and type in 'female Tanjiro x Rengoku' and you'll likely find a variety of stories with different themes and writing styles.
I'm not entirely sure as it could be a very specific and perhaps even a self - created or niche fanfic. It might involve a conflict or relationship between a character named Grunkle Ford Star and a dad character. But without reading the actual fanfic, it's hard to say more precisely.
One idea could be a rengoku fanfic where he trains a new group of young slayers. It could focus on his unique teaching methods and how he instills his values in them.