"Azula slept her way to the top"
But... isn't Azula already on top by virtue of being a fire nation princess? Who tf do these people think she slept with lmao
They unironically try to claim she fucked Ozai and/or Azulon to "earn" all that respect, praise, privilege and protection, ignoring that:
1 - She's a CHILD. A deeply awkward one that canonically doesn't know how to flirt. She's not sleeping around with ANYONE, any adults "involved" with her are not "pawns in her game", they're predators abusing her.
2 - These two men owed her protection and privilege whether they liked her or not (and Azulon clearly didn't) on the basis of "She's their child/grandchild." Her being safe, pampered and admired reflects well on them. It shows that they can afford to to give her the best teachers, best clothes, best food, etc. It's the same reason Ozai didn't get rid of Zuko until he had the perfect excuse to do so and why Azulon allowed them all to live in the palace despite clearly only "liking" Iroh (in his own fucked up way).
3 - Like you said, PRINCESS. Born at the top. Elite. She doesn't HAVE to do anything. If even Zuko could get respect every now and then on the basis of being a prince despite being a dysfigured, banished one, Azula, who was still living in absolute luxury with guards and servants waiting on her 24/7, sure wasn't struggling for it.
4 - Azula is a prodigy, the only person we see with blue fire, and clearly is good at battle strategy AND at playing the role of intimidating royal - all of which are much better at earning her respect and admiration than, you know, dishonoring herself, aka what her sleeping with anyone she wasn't married to would be seen as (doubly so as a princess)
5 - Azula very clearly took ZERO liberties with ANY Fire Lord and that does not suggest an incestuous dynamic. Hell, it doesn't even suggest a normal family dynamic. They were untouchable. Gods on Earth. The power they held over her, and everybody, was absolute. It doesn't matter if they're giving her the highest honors or nothing at all, her job is to bow before them saying "thank you for not killing me."
It's a classic case of "People just assign generic villainous traits to whatever evil character is in question, regardless of it making sense." Evil Seductress is a common role for female villains, therefore Azula MUST be one. I've said it once, I'll say it again, she could be wearing a burka 100% of the time and never have any interaction with any male character and someone, somewhere would still convince themselves she's the type of villain that gets it on with anybody.
Extra stupid when they use the bedroom scene in The Awakening as "proof" she's indeed a Femme Fatale that slept her way to the top, through her own family no less, ignoring that:
1 - Azula didn't sleep with Zuko, nor did she promise to or hint that she would. The tension is undeniable (thanks to Grey adoring the ship and getting the greenlight to voice it as she wanted), but neither Azula nor Zuko made a move because of course they didn't. It was not the writer's intention to go there, even if it was Grey's, so it is a moment of "...there's something weird going on here" that the narrative proceeds to ignore permanently because it wasn't part of the plan. Like a shared intrusive thought/mind in the gutter moment both characters refused to act on or even acknowledge.
And even ignoring production/intention, in universe, it makes sense that they didn't: Taboo, honor, rivalry, them both being awkward teenagers, Zuko's paranoia around Azula, Azula's need to be "perfect", etc.
Making Freud proud for a fleeting moment and then repressing the hell out of it to sleep at night is not the same as being a Femme Fatale.
2 - Even if we pretend they had sex or that Azula offered/implied she'd do it: Azula didn't GAIN anything out of that scene. Hell, she didn't even try.
She didn't get new information about the Avatar and how he might have survived (or Zuko's plans to deal with it), didn't find out about him visiting Iroh, didn't get any insight into his relationship with Mai or push him to make it more serious or break up with her, didn't find out about his Blue Spirit shenanigans or about his doubts and indentity crisis, didn't make him confirm her story to Ozai, NOTHING.
Hero X Villain romance/subtext does not make the villain an Evil Seductress when it's based on genuine attraction, without any machiavellian motivation.
3 - Zuko is bellow Ozai/Azulon in the Royal Family hierarchy, and depending on the day and circumstance, he's bellow Azula (not in the fun way). She was holding all the cards in that specific moment. Making a move on him would at best change nothing, and at worse would either ruin them both OR would be HER giving HIM a bit of power, as he'd know a shameful secret of hers and/or have something he knows she wants to use to his advantage, much like Azula used his need for Ozai's validation to her advantage.
Azula's behavior in that scene genuinely just cannot be seen as anything other than her toying with Zuko like she always does and things getting a bit strange because of the context - they're two teenagers that haven't lived under the same roof, let alone acted like siblings, for YEARS, and now they're suddenly all alone in her bedroom, at night, with her wearing just a robe.
They don't know where they stand with each other anymore. Their relationship is a confusing mess of contradictory feelings they can't properly identify, so pretty much everything, from "Why can't we just be a happy, normal family?" to "I wish you didn't exist and want to get rid of you", has crossed their thoughts. Some inappropriate stuff was bound to sneak in eventually.
And again, it's their minds (and ours, and Grey's) going there, not the plot, so even if we accept "They are attracted to each other" (and I sure do) that STILL does not mean Azula is this evil seductress using sex as a weapon against Zuko for power.