Okay, I must have totally missed the part where it was shown/implied that Ursa poisoned Azulon. Was that in the show or in the “sequel” comics?
There’s a lot of confusion surrounding this in general, mostly because some of the details in the show were semi-retconned by the comics - some of which lead to plot holes.
In the show, during the black sun mid-season finale, Ozai stalls for time until his bending comes back by talking about Ursa. And his explanation that Ursa found out Azulon ordered Zuko’s death, and came up with a sinister plot to attain the throne where Ozai said she did “viscous, treasonous things” to accomplish it in exchange for Zuko’s life - the main one being implied there that she personally killed Azulon. But it’s because of those treasonous acts that Ursa had to leave, both as a cover up and because Ozai didn’t trust her anymore on account of all the murder she did.
In the comics however, on the surface there’s a bunch of little changes to this to weasel out of having to have her murder someone personally, but lead to a 30 car pileup of plot holes when you actually think about it. Because it turns out her only contributions are thinking of the idea and making an “untraceable poison” (lol wut) for Ozai to slip to Azulon. She even says “you can do what you like with it” after she gives the poison to him, and leaves immediately after passing the vial off, just so she has the maximum amount of plausible deniability, but this means there’s a massive loophole in this deal she’s making because Ozai could easily choose not to use her poison, or not kill Azulon at all, and kill Zuko anyways and Ursa gave herself no way to actually stop this. Which was, you know, supposed to be the point of this plot. It doesn’t even really make sense for Ozai to do it himself, considering if he had Ursa do the murder he’d still be getting all the reward for the deed without taking in any of the risk in the event of failure. Plus if it’s an untraceable poison, and Ursa hated Ozai, why did she never consider slipping him some of that poison, then pushing his body down the stairs to make it look like he broke his neck in the 10+ years she was living there?
It seems like the comics were either Nickelodeon not wanting to show an on-screen murder, or Bryke wanting to erase the one patch of grey Ursa added by being a good guy who also killed a man, but either way it would’ve been better if they hadn’t backtracked and just left the show’s flashback alone. Especially since doing so also lead to a pretty big break from the show’s version thematically and character-wise considering the original point was to show Ursa’s willing to kill for the sake of love, and that she’s the real reason Zuko is next in line for the throne; and therefore becoming the Fire Lord is Zuko honoring his mother rather than his father. But between making her so uninvolved with the actual assassination, and all the letter bullshit making her original “never forget who you are” about Zuko questioning his paternal lineage rather than her emphasizing the importance of actions, they actually made it so now Zuko owes Ursa absolutely nothing.