Yes, he was.
Completely, epically, tragi-comically, absolutely out of character.
But then again, Zuko’s been out of character since the beginning of Book Three.
The first half where he desperately tries to be the son he feels he needs to be for Ozai to love him, and feeling horrible and alienated because, you know, he’s going against his nature as a kind, caring, sensitive individual;
And the second half where Zuko finds his inner peace and finally, finally becomes “the beautiful prince [he was] always meant to be”.
didshould’ve done* this by being all the different types of support to the Gaang that Iroh was to him.
Zuko’s field trips with the Gaang during Book Three were there so that he can recreate the different aspects of his relationship with Iroh:
First as the firebending teacher to Aang, then as unquestioning, absolute, physical and tactical support to Sokka and, finally, most importantly, as a guide on a journey of self-discovery and healing to Katara.
(This is also why when people go all: “Oooh, Zuko was enabling Katara’s worst during the “Southern Raiders”, ooooh” I go: “??? Reading? Comprehension? Do you have any??? At all???”**
Because if Zuko and Katara’s relationship during the “Southern Raiders” was “toxic”, then Zuko and Iroh’s relationship in, like, the whole show was as well.
Especially if you consider that one is two teenagers trying their best while the other is a grown man letting a 13 year old chase a ghost.)
Anyhow, to get back to your question Anon, that conversation with Toph was just the latest in a long line of writing decisions made to undermine Zuko’s character arc and core personality for the sake of a shallow, callous, and actually pretty cruel joke.
It could’ve been used to drive home the Zuko-as-Iroh-to-the-Gaang point by having him offer some kind of advice, paralleling Toph’s and Iroh’s scene from “The Chase”, especially considering that Zuko does, in fact, have the life experience dealing with a family which is never satisfied to be able to help her, at least a little.
But instead, you know, hahaha, moody-broody bad boy Zuko, we’re so funny and clever.
*The writing in Book Three is so inconsistent, you guys, it’s so. Not. Fair.
** Which, granted, may be a bit unkind, since the writers are actively trying to sabotage any and all character development throughout season three. Still!