He then apologizes to Nezuko about everything he had done to her in the past and that he was asleep the entire time after the defeat of Muzan.
And that I was brave.
I can make really good ones.
This endears her to Tamayo, as she is touched by the fact that Nezuko views her as a normal person, despite her status as a Demon and her past sins.
Inosuke sees Zenitsu as annoying, loud, weak initially , and a crybaby; while Zenitsu sees Inosuke as a violent moron who's only interested in fighting.
When Nezuko gets in danger fighting against the train demon, Zenitsu jumps to rescue her in his sleep, claiming he will protect her.