I've seen people scoff at the idea that Zuko became the most mature member of the gaang when he joined and I gotta wonder if they haven't watched the show for a while or just aren't using their analytical skills, because he absolutely was, and its not just his age because Katara was second most mature compared to him and she's younger than Sokka.
No, it's cause he's a prince who has led people before, who has been shown even in the first season as a villain to have boundaries he will not cross and to put the lives and safety of those under his command before anything else.
He's also the only one of them to have had an actual adult imposing wisdom and guidance on him that he is basing his behavior on, the rest of them are pretty much self-taught. Toph was coddled and suffocated by her parents, Katara and Sokka had an absent father and were raised by their grandmother who did her best but they also raised themselves and each other, Aang had Gyatso and the other monks but he was also only 12 and was very immature (non-derogatory). By the time Zuko joins the gaang he has fully embraced Iroh's lessons, he's abandoned any attempt at being the son his father wanted and is choosing to live by the lessons Iroh taught him. He's emulating a strong adult role model that the rest of them didn't have the same access to.
Immediately upon joining them he's taking initiative and taking care of the other kids, we see him being the one trying to keep everyone on track, the one putting his body on the line to protect everyone else, he's being very observant of the other kids' thoughts and feelings and anticipating their next moves or their needs. He's staying awake to catch Sokka before he can do something stupid like flying Appa to Fire Nation Alcatraz alone. He's staying up all night outside Katara's tent just cause he wants to help her get closure for her grief.
He's babysitting them like Katara would except he's got official leadership skills and has commanded actual soldiers whereas Katara, bless her, was parentified and self-taught in her leadership skills, which is also one of the reasons that Zuko joining gave Katara a reprieve from being the one holding everyone together, and brought out her angst and unaddressed grief, not just because she was holding onto her anger at Zuko's betrayal but also because him becoming the responsible one took a burden off her shoulders. Even though she was still mad at him, having him there and taking charge meant that she had more time to look inward and stew in her darker emotions, because she no longer needed to put everyone else first for the sake of the group.
He's the one they all turn to when they're not sure how to proceed. He asks "Why are you all looking at me?" after Aang disappears and they say something about how he's basically the expert on tracking down Aang (lol) but it's more than that. Since joining he's become the guy who comes up with all the major schemes. He helped them accomplish things they wouldn't have been able to do without his help, he is a good planner and a good leader because unlike the rest of them he has actual official leadership skills, he knows how to be authoritative and boss them around, in a good way. They trust him to lead them.
He's acting like Aang's drill sergeant, picking him up by the scruff of his tunic like an unruly kitten and dragging him back to training.
He's crashing out big time over the fact he's sending an underprepared pacifistic child to face his (Zuko's) abuser, the guy who melted half of his own son's face off. Even when on his way to face Azula, it's not himself he's worried about, it's Aang. When he sees the chance to face Azula alone without having to endanger Katara, he takes it.
The moment Zuko joins them, he puts the others first, prioritizes their needs over his own, goes out of his way to help and protect them at the cost of his own safety and wellbeing. He literally almost dies for Katara and is still only concerned with protecting her while he's on the ground convulsing and clinging to life after being electrocuted.
Zuko is without question the most mature member of the gaang when he joins them. He is the older brother. When he joined them he became a teen dad to three adopted kids, got divorced to Katara and started co-parenting them all with her until they made up and became friends again, which again was a conflict that he took the initiative to solve without expecting anything from her.


















