His relationships could also be a source of depressive themes. For example, if he has a falling - out with Katara or any of his close friends, it could lead to a downward spiral of emotions. Or perhaps the guilt he feels for not being able to save someone or for making a wrong decision in a battle can be explored in 'aang depressed fanfiction'.
Another theme might be his loneliness. Aang was the last airbender for a long time. He may feel isolated even among his friends because they can't fully understand what it's like to be the sole survivor of his nation. This sense of loneliness can contribute to his depression in fanfiction.
One common theme is Tenzin learning from Aang. Since Aang was Tenzin's father and also a great Avatar, many fanfictions explore how Tenzin grew under Aang's guidance. For example, Aang teaching Tenzin about airbending techniques or the spiritual side of being an airbender.
One common theme is isolation. Stiles might be shown as isolating himself from his friends and family due to his depression. For example, he could stop going to school or social events.
One common theme could be isolation. Mineta might be depicted as being alone due to his depression, pushed away by his peers or feeling like he doesn't fit in. Another theme could be self - loathing, where he constantly criticizes himself for his actions or his personality traits.
I'm not sure about specific 'Aang depressed fanfiction' offhand. You could try searching on fanfiction websites like Archive of Our Own. They usually have a large collection of Avatar - The Last Airbender fanfictions, and you might be able to find ones related to Aang being depressed by using relevant search terms.
One common theme is friendship. Since they come from different backgrounds in the Avatar universe, exploring their growing friendship can be interesting. Another theme could be adventure, as they might go on quests or face challenges together. Also, there could be a theme of cultural exchange, with Aang being an Air Nomad and Onji being from the Earth Kingdom.
One common theme is self - discovery. Aang often has to look within himself to find the path to enlightenment. Another theme is the connection to the spirit world. Since Aang is the Avatar, his enlightenment is closely tied to his understanding of the spirit world.
One common theme is the corruption of Aang's pure heart. Since he was the Avatar, a symbol of peace and balance, seeing him corrupted by dark forces creates a strong contrast. Another theme is the struggle between light and dark within him. He has to fight his own inner demons.
One common theme could be self - discovery. Aang having hair might be seen as a new part of his identity, and fanfictions could explore how he comes to terms with this change. For example, he might have to deal with how others perceive him differently.
One common theme is redemption. Many fanfictions explore Azula's journey towards redemption, often with Aang as the catalyst. Since Aang is a very empathetic character, he is often the one to reach out to Azula in these stories.
One common theme is friendship. Since they start off as enemies, many fanfictions focus on how they build a strong bond of friendship. Another is redemption. Zuko's journey of redemption is often explored further in relation to Aang.