Sokka: No, his arc is about taking himself too seriously to the point of making himself ridiculous in his attempt to emulate what he think he must be now that all the adults are gone: A leader. Something Katara also goes through to a lesser extent in the prisoner episode. So not only gender isn't fundamentally his arc, it's basically irrelevant to it.
Suki: What gender complication does she add to Sokka's understanding of gender in the Boiling Rock episode and every other episode afterward? None? Okay. Her serving a point in ONE episode does not make it her whole arc, let alone fundamentally.
Katara: Her being meant as an ideal girl does not make her arc fundamentally about gender, it just mean that's the type of character she is. Having your arc FUNDAMENTALLY about gender does not mean 'You're a certain type of woman', that's a character archetype, not an arc. And no, Katara didn't suddenly become a blank slate after fighting Pakku, she has an arc about each of her missing parents all the way to book 3 FFS.
Yue: We're just gonna ignore she's also a literal resurected chosen one of the moon spirit and her relationship with Sokka is based on finding him funny to be around? Okay.
Toph: It's so her entire point she was planned to be a boy for most of pre-production. Her 'rebellion' wasn't against gender norms, her rebellion was against her parents' obsession with her safety and inability to trust her due to being blind and thus 'helpless'. Toph as a tiny 12 year old boy would have been treated the same and was literally PLANNED that way to begin with. Again, not only not 'fundamental' but entirely irrelevant.
Zuko: No, this headcanon needs to die, Ozai wasn't gonna go 'Well done, son' if Zuko tried to fight him at the Agni Kai, he'd have gotten mad, beat the shit out of him, burned him and banished him. That's why it's abuse, there was no winning the moment Ozai decided Zuko fucked up and needed to be taught a lesson. And no, honor isn't manhood nor are honor duels, you mention Zuko's first Agni Kai while ignoring his last AGAINST A WOMAN, which NOBODY BATS AN EYE about and the lore tell us the Girl's Academy has Agni Kais all the time.
Azula: No, she's not, she's playing the role of the perfect princess and that's it. And no, nobody particularly react to Azula as a girl. And none of that make her arc fundamentally about gender.
Ty Lee: So by your own admission her arc isn't about gender at all, everything else you said is irrelevant and doesn't make her arc fundamentally about gender. Also she does have an arc, it just mostly get resolved offscreen cause she's a tertiary character, her getting over her 'matched set' worries and joining the Kyoshi Warriors is her arc's conclusion.
Mai: Except it's not? At all? For a single second? There's no line saying that in the entire franchise. Her arc is about being mad she can get whatever she wants and DO whatever she wants as long as she stays out of the way. It's about neglect and can (and does) happen the exact same to a boy, not about 'muh gender roles'.
Smellerbee: Yes, you do have to make an argument for your point. A character being mistaken for a boy as a running gag doesn't make it their arc, it make it their running gag. Smellerbee's (very minor) arc is about being a follower of Jet, going from an unthinking yes-woman to someone genuinely supporting Jet in the aftermath of their mistake to someone who now need to make their own way cause their leader died trying to make things right.
And yet everyone you named didn't have their arc fundamentally about gender at all and you could say the exact same stuff you said about the other characters about Aang and Jet (Aang wouldn't even have been raised by Gyatso nor lived in that part of the world if he was a girl and Jet is literally a classic manly man suave Robin Hood leader type, which wouldn't work if he was a woman).
Seriously, this take is pure Tumblr gender discourse brainrot and completely disconnected from the actual show. Come on.