Speaking of applying logic, that's what we typically do through science studies, which consistently show that other animals experience emotion and self-awareness to far higher degrees than previously understood.

asking about one’s character and goals, is likely unique to humans in my view.

I agree that modern man likely has the most articulated language that's ever existed on earth, which is a big part of that. But would hunter-gatherers have asked themselves about their 'character and goals' as part of their regular life? I don't know that such would be the case especially more than other humans or apes did or do. That said, keeping a nomadic, tool-using tribe going arguably would have required more of that than at any other level of organisation.

Which again suggests to me that a big part of that impetus comes from the level of civilisation I described. I think that's really what you're thinking of. Which hardly correlates to our genes at all.