Tanjirou is not a direct descendant of the Breath of the Sun users.
He is an inheritor of the TECHNIQUE. That very same Kagura Fire Dance Tanjirou memorized as a child is the same.
One of Tanjiro's ancestors was a friend to one of the original Sun users, who was most likely Kokushibou's twin brother.
Yoriichi did not have a family of his own to which he could pass down the technique, so he taught it to Tanjirou's ancestor with the promise that they would pass it down through their descendants.
And by perhaps, 'fate', the very blade of Tanjirou's current sword belonged to Yoriichi.
It would be pretty neat if Kokushibou and Tanjirou could meet - the latter being a split image of Yoriichi(younger) were the former able to see him.
But it's not meant to be; Tanjirou and Giyuu are supposed to continue heading towards Muzan...
And UM4 looks to be hands-down one of, if not, the most terrifying of the Demon Moons... the weak, but VERY annoying type. The one that makes many a person rage quit...