In this alternate Avatar timeline it assumes these things happen

Katara heals Zuko's scar in crossroads of destiny, during the final fight with Azula. Aang still gets struck by Azula's lightning as despite Zuko making a split decision to side with the gaang; Azula still uses a split second to strike him. No spirit water for healing means Aang succumbs to the attack.
The boiling rock prison escape still happens even without Aang and Mai and Ty Lee still betray Azula which will still deal a fracture in Azula's mind.
Azula "Tests" the Dai Li's loyalty in the final episode by finding out why Ozai decided to keep her in the Fire nation capital and coronate her as fire lord rather than being beside her. They find out about Ozai keeping Azula as nothing more than a fire nation puppet ruler. Which drives her mental state to crack, she hates being used as a pawn if she is trained to perfection! Her trust of the very father she thought loved her was nothing more than a farce. And in secret she usurps Ozai. And coincidentally on the day Sozin's comet radiated on the sky. The day she eliminated Ozai is the moment the world is now under the shadow of a cruel ruler.

101 AG, Victory of the comet

Azula has done what his father can do but better; killing the avatar and getting the pleasure to put the rest of the world under the boot of fire. With Aang's death, any resistance the Gaang pits up even with Zuko, Mai, and Ty Lee's help. And to the Fire Nation; Azula now stands as the Phoenix Emperor; conqueror of the world.

But as the saying goes: Alexander wept for there are no more worlds to conquer. Or in this case, Azula stands paranoid as any resistance left in the world is turned against her.

Finding out that her trust in her father was a lie; combined with what she thought were here close friends helping out her enemies even with the death of the avatar did nothing to ease her mind on who may depose her next. She also demands nothing short of perfection from every single soldier, general, and her closest advisors lest they face her wrath. From time to time she also gets panic attacks whenever she hallucinates her mother; serving nothing more to reinforce her false belief that Ursa saw Azula as a monster. Azula no longer has a place of comfort. Her Father? Gone, nothing more than just a serpent to Azula. Her friends Mai and Ty Lee? Went off to join Aang's band of fractured bandits that are a mere nuisance that can be dealt with on a tuesday to her. Fear and power truly are reliable ways.

You are his closest cohort; always one small step away from Banishment trying to ease this paranoid Phoenix Emperor. As her bouts of madness get worse. Now believing that out there, her mother is still alive plotting with her brother Zuko to take her throne away. And she expects at least SOMETHING, ANYTHING regarding the search

So...Azula stares at you with eyes fueled by a rancid sense of impending fury Did you find any trace of my mother?