She only goes into his office when Zuko is there. It's not just because the guards and servants give her far less freedom when Zuko is gone than they let on either. It just feels wrong being in there without Zuko. Too easy to sit at the chair and pretend she is Firelord and she knows nothing good will come of that. Sometimes she thinks losing the war was the best thing that ever happened to her; there is a strange freedom that comes when the weight of expectation is lifted. When Zuko is sitting in his office it's safe to enter and so she does because she can. Because Zuko won't deny her the right to sit and watch him go through his papers.
She snipes at him out of habit more than anything else. Habit and the strange longing that builds in her chest once she realizes his personal correspondences really are personal. They aren't letters from Generals or Overseers, they're from his friends. She wonders if she ever truly had friends or if that was just a lie Mai and Ty Lee were too afraid to expose. Sometimes when he puts a letter to the side she'll steal it off the pile and read it; learning of Ty Lee's adventures on Kyoshi Island and Uncle's tea shop. It's petty and more than a little pathetic, but she likes to pretend they are writing to her.
Slowly, so slowly she doesn't even notice it, Zuko carves out a space for her in his office. A chair and a table and a standing tea order don't seem like much, but somehow she only notices when the writing materials show up next to a letter from Uncle Iroh. They're both waiting for her when she wanders in for her daily dose of poking at Zuko. Her hand is trembling when she picks up the letter and somehow the simple correspondences, the generic greeting and well wishes from a man she treated horribly are enough to send her to tears.
She barely notices when Zuko hugs her in his awkward way, too busy staring at the letter, but eventually she finds herself clinging to him. He rubs her back as she finally mourns all the things she sacrificed to be the daughter Ozai wanted. It's ultimately as uncomfortable as any of their attempts at being nice to each other, but she still somehow feels better by the end.
They don't speak of it later. She responds to Uncle Iroh and reads Zuko's letters and starts collecting a small shelf of books in her corner of the office. One day she receives a letter from Aang of all people that she stares at in bewilderment for far too long. Another day she gets one from Toph, who at least admits that Zuko asked her to write. She's not sure what to do with these pity correspondences, but she replies nonetheless. It's something to do.
It's not until she's meandering through the halls on New Years, smudging paper lanterns, that she discovers the hidden truth and the dirty trick Zuko played on her. Aang finds her in an alcove and watches as she draws senseless designs on the thin paper before laughing. She's ready to yell at him, to tear him to pieces verbally, when he walks up to the next one in line and carefully copies what she'd been doing. He misjudges something and the whole lantern goes up in flames.
They stare at each other for a second as the last bits of ash fall to the ground before busting into laughter. It's only then, as she teaches Aang the proper way to smudge paper lanterns, that she understands the gift Zuko has given her.