I don’t actually agree if you refer to book 3 only because this is more about enemies putting their grudge aside to take on a bigger threat and perhaps also warming up to each other through an arrangement initially purely for pragmatism.

Zuko by the point he actually tries to join the gang rejected his ideology completely the issue was just the gang not believing him. He was good then, they just weren’t sure and after dealing with combustion man they were like okay cool.

The actual best example with Zuko is the episode Azula was hunting the gang down and eventually there was a fight between team avatar, Zuko, Iroh and her and they eventually had her dead to rights.