I never told you I was lonely too

Someone will read it

The most salient example of this is probably when she tries to recruit Ty Lee to her mission. After Ty Lee refuses her initial (and very casual, I might add) request, Azula immediately pivots to the tools of fear and coercion, entirely bypassing something that probably would have been much more effective—actual honesty and vulnerability.

Had Azula just leveled with Ty Lee—told her that her father tasked her with something important and it hadn't been going well so far, and that Ty Lee was one of very few people she trusted to help her get it done (maybe even that she was a little scared of what might happen if she didn't succeed)—I don't think there's a version of events where she still says no.

Instead, Azula begins with an appeal to Ty Lee's self interest (ie. Aren't you tired of this?/Don't you want to get out of here?) and when that doesn't work, she goes straight to intimidation because she doesn't trust that her friend loves her enough to willingly make a sacrifice for her sake when that is literally what friends do!