Speaking about Azula ships, Azurin (Azula & Zirin, the girl from the asylum) is her most underrated ship, and Zirin, despite how little we know about her, is a very good candidate for Azula’s first true friend and/or love interest. I mean how little we know about her is the best thing actually, as she already has a long history with Azula but you still can make her anything.
Some reasons why they could easily bond in the future:
Zirin isn’t afraid to be honest with Azula and question her. (She speaks openly in SS and goes against her in AitST, yet without trying to harm Azula or put her down.) And that’s actually exactly what Azula seeks — that’s why she threw this social experiment with being incognito on Ember Island: to check her inner suspicions of being a monster and see how people view her as a person without the “protection” of a title. So, Zirin effortlessly gives her honesty.
Zirin has a huge reason to be very grateful to Azula, as she saved her from a place where girls were treated inhumanly for not being obedient enough for their families. And she is — she helps Azula with her mission.
Both Zirin and Azula share the same “enemy” — terrible external factors that bring them closer and encourage them to work together and treat each other with sympathy: the asylum. No one in Azula’s circle experienced this level of unfairness during imprisonment of any kind — Zuko, Mai, Ty Lee, Suki, Iroh, Katara, Toph, Ozai, and Ursa all had at least freedom of movement, and sometimes the freedom of bending or living in a freaking palace during their periods of imprisonment. Only with Zirin does Azula share the experience of literally being tortured during their imprisonment. Shared negative experiences add a level of sympathy and understanding.
The people who put them into torture are their very families (the asylum was used to throw away disobedient daughters). The family is the torturer, which adds an even deeper level of shared negative experience and potential bonding over that. Azula especially has trauma over her mother’s lack of love/showing love, personal interest, and approval of her. And Zirin’s mother is either dead or didn’t mind/stop her from being put into the asylum. Zirin might very well understand Azula’s maternal trauma.
Zirin is loyal. Something Azula very much is herself, and something she respects. Zirin’s desire to save a friend who got captured will actually seem like a positive trait from Azula’s POV after she (partially) drops her ways of controlling people with fear/status/them owing her their freedom, which she does in AitST when she lets them be instead of imposing her will on them.
Zirin is a Fire Nation noble, so despite still being far in status from a princess, they are products of the same culture and do not have to reinvent the world to understand each other’s conditions.
With Azula learning in AitST how to leave people to themselves and not drag them after herself (even if she believes she means good for them), she could develop a friendship or a closer relationship with a person who doesn’t have a history of bad or mixed feelings towards her, has a reason to be grateful to her, with whom she shares the most horrid experiences, and who understands having a family that doesn’t give a fuck about your well-being and is happy to throw you away once you step out of line.
There is a lot of ground upon which they would find each other deserving of sympathy. Despite the Fire Warriors leaving her in AitST, it’s not as painful for Azula as Mai, Ty Lee, and Zuko’s betrayal, as the girls didn’t do any harm to her in the process (they could have killed her during her sleep, for example, or handed her over to the officials), and their decision kind of made her rise above herself rather than sent her into a temporary loss of mind, which is a positive new thing for her, meaning positive associations.
Azula would appreciate having someone outside of her princess/child-soldier experience with whom she could talk about her buried pain and struggles and receive something more than ignorance as an answer, as Zirin shares essentially the same or very similar problems. Azula would also appreciate her honesty and fidelity while maintaining her newer achievement of not commanding her friends around and building a relationship (based on shared bad experiences in the past) on a voluntary basis.
So if they meet again (and there are tons of scenarios in which they might meet again), they very well might bond and do ship-worthy things.
Bonus: as we barely know Zirin, you can write/draw her character to be anything you like in whatever surroundings (with them having any kind of positive or negative relationships with other characters). Azurin has no limitations! It can be:
two wanted assassins in a relationship
fucking off to the Spirit World to have a Miyazaki-type adventure
Sherlock and Watson but with no Mary to bother them, so they could actually fuck
a minister of some sort and her gf throwing the maddest lesbian showings at official events
Of course, anyone can ship anything, and all Azula ships are nice (they have Azula in them, after all), but Azurin is really underused!