"Zutara is girl-fixes-boy trope"
NO. Zutara is a subversion of that trope.
In canon after Katara offers to 'fix' Zuko, he betrays her; then he fixes HIMSELF and helps Katara find closure from her trauma
"Zuko and Katara would be toxic and fight all the time cause they're both prone to anger!" You're just projecting cause this is Zuko when Katara is mad at him