You can try Archive of Our Own (AO3). It has a vast collection of fanfiction from various fandoms, and there's a good chance you'll find aang abandoned fanfiction there.
One could start by looking on popular fanfiction platforms. Some might be about Aang's journey after being separated from his friends for a long time. Maybe there are stories where he has to face new challenges alone in a strange land.
He could meet his future self. It would be an interesting encounter as he could learn from his future experiences and wisdom. Or he might meet people who have studied his past adventures and see himself through their eyes.
Possibly they are random villagers who were caught in the crossfire of a conflict between different bending factions. Aang, being the Avatar and a symbol of peace, feels responsible for burying them and ensuring their spirits are at peace.
He might start by observing. Aang is a curious person, so he'd likely watch how people live, how they interact with technology. He may also try to find other benders to learn about any new developments in bending. And he'd probably use his kind heart to make friends easily in this new future environment.
Sokka could be one of the main characters. He might be the one helping Aang with his schoolwork, especially in subjects like history or math, using his own knowledge and quick thinking.
Aang might go into a deep state of depression. He has always been an emotional character, and having his heart broken by Katara, someone he loves deeply, could send him into a downward spiral. He might isolate himself from his friends and stop practicing his bending for a while.
In some fanfictions, Aang's connection to his past lives plays a crucial role. He could draw on the wisdom and skills of previous Avatars. They might guide him on how to defeat Azula specifically. He could learn a new bending technique from one of his past lives that gives him an edge over Azula's firebending, like a unique way of using water to extinguish her most powerful fire blasts.
Well, Aang being the Avatar has a deep connection with the elements. In this fanfiction, perhaps he enters the Avatar State and uses all his elemental powers in harmony. He could use waterbending to create moisture and cool the volcano, combined with his airbending to disperse the heat and gases.