Let's assume that a character is not given a lot of story

just bits and pieces

so therefore, I made up a story that attempts to tie up the little hints of the stories of the character, including storylines of other characters that interacts with the aforementioned character

so, in this case, would this be defined as an OC or an AU

Neither, it's extensive headcanon.

keep in mind I'm keeping the appearance and powers as presented in the small stories

hmm, you would still define it as a canon character?

If the character appeared in the canon then yes, I would. I wouldn't say that necessarily makes him more appable, but I don't think OC covers it if it's not your creation.

close to a 'canon oc' definition, imho

welp, time for iidx beatmania apps

yeah, if its a loooot of headcanon based on speculation its most like a canon oc

I was so happy when they had stories for their songs and then I realised it was just a silly thing they wrote about how the composers came up with the song

You're thinking of Vocaloid, or something similar to that?

something similiar, yes

scroll down until you get to PROG ROCK

EPIC PROG, I meant, whoops