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.
Webnezuko seems ambivalent about zenitsu’s constant stream of love confessions and dramatic proposals.
She tolerates his overt displays of infatuation, but.
Webno, at least not in real life.
Zenitsu would probably make a girl like nezuko really uncomfortable with how much he simps after girls and her especially.
(demon slayer / kimetsu no yaiba)want to.