Tanjiro and Senjuro’s bond
Even though Senjuro told Tanjiro that he would send Kaname if he learned anything new about Sun Breathing I would wager that Tanjiro was the one who sent a letter first and started the penpal set up between them. We saw in the Entertainment District Arc that when Tanjiro thinks about Kyojuro he also tends to think about Senjuro and Shinjuro. Visiting the Rengoku Estate, and especially talking with Senjuro, played a huge role in Tanjiro working through his grief and getting out of his depression. And in only a couple of hours of knowing Senjuro --if not less--just like he did with Kyojuro, Tanjiro grew attached to the younger Rengoku. I could see Senjuro being a little nervous when Tanjiro’s crow shows up first, because he hasn’t found out anything yet, it’s only been a couple weeks.
But instead Senjuro gets a letter not asking about the research at all. Instead it’s full of : How are he and his father doing? Is Shinjuro being nice to him? Does Shinjuro hate his guts because of him head-butting him into unconsciousness? He still feels awful about that. Is there someone who needs a Headbutt? Was Senjuro still struggling with his grief from losing Kyojuro? Tanjiro is thinking of him, of Shinjuro and still thinking of Kyojuro, he hasn’t forgotten Kyojuro-aniki or his new resolve. And there’s nothing at all asking about Senjuro doing research for him. Because just like Kyojuro, Tanjiro cares about Senjuro as a person, and not what Senjuro can “give or contribute”.
As a sibling himself, and having had to wait two years for Nezuko to wake up, basically being separated from her in a sense because she was unconscious--and also having had family killed--Tanjiro would understand and be able to truly empathize with Senjuro’s feelings of loneliness and missing his brother. Senjuro is one of the first new friends that Tanjiro made who wasn’t an active member of the corp. He doesn’t get to see him as often, and even though Tanjiro understands why Senjuro can’t come with them, he probably still wishes that Senjuro could. But since he can’t, the closest Tanjiro can do is sharing stories with him.
Tanjiro shares Kyojuro’s traits of being inquisitive and earnest, he would be curious about what Senjuro is up to and I could see him wanting Sejuro to tell him in depth about his day, his schoolwork, etc even if it seemed “trivial”. Because like Kyojuro, to Tanjiro it’s not trivial. What is going on with Senjuro, what Senjuro cares about matters a lot to Tanjiro. He would be excited about Senjuro’s achievements in school and what he’s learning about, and still be gentle about whatever emotional struggle Senjuro decided to share with him. Kyojuro can no longer be here in person for him, so Tanjiro makes sure that he can, to the best of his ability. I wouldn’t be surprised if Senjuro was the person that Tanjiro was transparent with about his struggles and feelings. He and Senjuro in that first visit had a very emotional conversation where they shared vulnerability with each other, and it was a positive experience. Because of that they would be more comfortable and willing to be emotionally honest and vulnerable with each other. In a way that Tanjiro probably can’t do as often with Zenitsu and Inosuke--Senjuro is on a different maturity level than both of them, and closer to Tanjiro’s maturity. And think about what that means for Senjuro and how it must make him feel. He gets to support Tanjiro emotionally the way that Kyojuro did for him, and in a way he probably felt he didn’t for Kyojuro, he gets to share wisdom that Kyojuro taught him. And even though Tanjiro is an older brother like Kyojuro, because of his relationship with Kyojuro, he gets to see almost eye to eye with Senjuro just as much as with Kyojuro. They were both younger brothers to Kyojuro, so Tanjiro understands Senjuro on that level now, and vice versa. I love so much that Tanjiro didn’t come to care for Senjuro out of sympathy, or just because he was Kyojuro’s little brother but from having a genuine connection with him and making that conscious decision to build on that relationship.