Nezuko and zenitsu do end up together, as hinted by the manga's finale.
However, it's not explicitly shown how the two end up.
It's a healthy friendship.
Webin the animanga series, romance takes a back seat.
However, there are pieces of evidence in the manga that suggest characters have love interests.
Webone character who openly shows romantic interest in nezuko is the crybaby demon slayer zenitsu agatsuma.
From the moment he lays eyes on nezuko, zenitsu is.