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.
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.
Another way Percy could react is by giving Annabeth the silent treatment. He wouldn't talk to her for a while, which would be really difficult for Annabeth as they are usually close. Percy would just go about his business, ignoring her attempts to communicate until he feels she has truly understood how much she has angered him.
He might become withdrawn at first. Since he's used to being in control and having a certain dynamic in their relationship, Bella's anger could shock him into pulling back. He could go off on his own for a while to think about what he did wrong.
Yes, in some fanfictions, Tanjiro is depicted as the reincarnation of Yoriichi. This concept adds an interesting layer to the story as Yoriichi was an extremely powerful and legendary figure in the original lore. The idea allows for new storylines where Tanjiro might inherit some of Yoriichi's skills or have a deeper connection to the past events related to Yoriichi.