for me, when considering au versions of a character, it basically comes down to: (1) what fundamental characteristics stay, regardless of change? (2) how are their beliefs and their inner world shaped by their alternate circumstances?
let’s consider the case for izuku. for question no. 1, i’d say that some facets of his personality that stay regardless of the universe are:
- his tendency to fixate on a subject/topic of interest, which often becomes a driving passion as well. mostly: he’s a nerd who will write, color code, and organize 13 notebooks on heroism if that’s what interests him. although his interests may change between universes, how he engages with them does not.
- his tendency to avoid or escape from his own problems, even though he knows he shouldn’t
- tendency to devalue himself (this is usually tied to the years of bullying & abuse he suffered at bakugou’s hands)
- alarming proclivity to go “self harm is okay then?” and do something extremely inadvisable for himself in pursuit of a goal (which is, more often than not, helping someone else)
- this is because izuku considers his health and well-being as a tool he has to be used in pursuit of a goal, rather than a goal in and of itself
- quick thinking and analysis, as well as some sarcastic quips if he feels comfortable at the time
- loves his friends and family, would do just about anything for them
- an unshakeable conviction and impulse to act when concerning his beliefs. he may be nervous, afraid, unwilling, etc. in any other situation or when it comes to protecting himself; but put him in a situation where someone is out of line with his beliefs, and he will act. (i.e. in canon, compare izuku’s normal demeanor with when he yells at todo/roki and i/nasa to get over themselves and get a-heroing. top 10 anime scenes)
so then we have a very good idea of the skeleton of izuku’s personality. we then flesh it out with changes rendered by an au, and consider question (2).