you get by id first and then pass the current value to the new Todo instance:

pub fn update_todo_by_id(&self, id: &str, todo: Todo) -> Option<Todo> {
    let mut todos = self.todos.lock().unwrap();
    let updated_at = Utc::now();
    let index = todos.iter().position(|todo| todo.id == Some(id.to_string()))?;
    let todo = Todo {
        id: Some(id.to_string()),
        updated_at: Some(updated_at),
        created_at: todos[index].created_at,
        ..todo
    };
    todos[index] = todo.clone();
    Some(todo)
}