The Hashiras would likely show concern. Some, like Shinobu, would immediately start looking into possible medical solutions. Giyuu might be more reserved in his worry but would still keep a close eye on Tanjiro. The other demon slayers would also be affected. They look up to Tanjiro, so his sickness would lower the morale of the group. They would try to support each other while waiting for Tanjiro to recover.
One common theme is his growth as a sorcerer. Many fanfics focus on how he hones his skills and becomes stronger. Another theme is his relationships, like his friendship with Yuji or his complex connection with the Zenin family.
There's a fanfic called 'Megumi Fushiguro: A Different Path'. In this, the author takes Megumi on a completely different adventure from the original story line. It's really interesting to see how his character develops in this new scenario. Also, 'Megumi's Hidden Powers' is a fanfic that uncovers some potential powers that Megumi could have, which makes for an exciting read.
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.