Okay, so I've been down this rabbit hole more times than I care to admit. The landscape for Azula-centric reader inserts has changed a lot over the years. It used to be that FanFiction.net was the only real hub, and you could find some absolute classics there if you dug through the endless Zutara fluff. The tagging system on that site is a nightmare, though; you really have to rely on the 'Azula' and 'Reader' tags and then filter out the non-insert stuff manually.
These days, the epicenter for quality Azula x Reader content has almost entirely migrated to Archive of Our Own. The search and filter functions are just superior. You can easily exclude other pairings, specify for 'Reader-Insert,' and even sort by kudos or comments. The culture on AO3 also tends to produce more nuanced, in-character Azula portrayals. You'll find fewer 'bad girl gone soft' stories and more explorations of her complex psychology, where the reader character has to navigate her manipulation and ambition. The quality control is simply better, with writers who clearly understand her as more than just a goth girlfriend.
Don't sleep on Tumblr, however. It's a different beast. A lot of the content there is shorter, more prompt-based, and lives in individual blogs. You find gems by following specific Azula-centric writers who post drabbles and headcanons. The interaction is more direct, and you can sometimes request scenarios. The downside is discoverability—it's a fragmented archive unless someone's compiled a masterlist. Wattpad has some, but the writing quality varies wildly, and it's buried under a mountain of other 'bad boy' romance templates that don't fit Azula's vibe at all.