Well, without more context, it's difficult to say precisely. 'Appa' could be a person, an animal, or even a made - up creature in this fanfic. The act of eating cabbage could be symbolic, like representing a simple life or a particular cultural aspect if there are more elements in the story related to a certain culture. Maybe it's a comical fanfic where the way 'appa' eats cabbage is really funny.
I'm not sure specifically as I haven't read this particular fanfic. It could potentially be about Aang dealing with the loss of Appa in a very emotional way, like burying him, and perhaps exploring themes of grief, friendship, and the bond they had.
Character development is key. In good fanfiction, we might see Aang grow in his understanding of Appa's needs and vice versa. Also, an engaging plot that takes them on new adventures, like exploring uncharted regions or facing new enemies, makes for great fanfiction. It should also be true to the original spirit of the characters from the source material.
Since I'm not entirely sure about this specific fanfic, but generally in Avatar: The Last Airbender fanfics, themes could include friendship, adventure, and the power of the elements. If 'buryinv' is a new character, perhaps themes could revolve around how they interact with aang and appa, like learning to trust each other.
You can try some fanfic platforms like Archive of Our Own (AO3). It has a wide range of fanfics, including those about appa shownu. Another option is Wattpad, which also has a large collection of fan - created stories.