Ok, I think I see you mean "outcome" as an eventual behavioural manifestation, and by "trait" you mean a biologically inherited property or feature or capability, at least roughly.
> Do we have a part of our brain that no other animal has, or could have, that means we can become literate and no other animal ever could?
I think clearly yes, depending on what you mean by "could have". I wouldn't rule out the possibility that somehow over evolutionary time some other animals might be able to reproduce human behaviours of reading and writing. But I'm not talking about that: I'm talking about what other animals can do now, and it seems none of them can write or read like a human.
Now, let's say there are chimpanzees that we can teach to respond appropriately to things like "Spot has a ball. Spot has a big red ball. What colour is Spot's ball> Blue or Red?" Maybe they can do that. But what about doing the exercises in, say, Loring Tu's Introduction to Manifolds? They're just not doing that. They don't come close. You might say most humans aren't doing that either, which is true, but if you train a human their whole life in an appropriate way then I think most of them can do at least some of those exercises, while no chimp or bonobo has been shown to have this facility. This is just one almost silly example, but I think you can see what I'm getting at.
> Dolphins being able to see your organs by clicking is pretty fucking exceptional. But because humans can't do it, it's not "exceptional."
If this is unique to dolphins, I would say it's definitely exceptional. Even if it's not unique to dolphins, but only a small subset of animals can do it, it's still exceptional to that small subset of animals. There's no reason why "exceptional" should pertain only to one species: different species are exceptional in different ways, and we're asking in this thread about whether and how humans are exceptional. Horseshoe crabs are also exceptional in that they've been physiologically constant for 200 million years or whatever it is. The fact that some species are exceptional in their own ways doesn't mean that humans aren't exceptional in their own ways.
> The fact that our combined traits allowed for different outcomes doesn't make us fundamentally different any more than a frog is different to a cat.
I think I can see what you're getting at: every animal is arguably exceptional in its own way, and picking out the ways in which humans are exceptional as being more significant than others is stacking the deck in favour of finding humans to be uniquely (or exceptionally) exceptional in an anthropocentric way.
It's definitely right to be aware of, and cautious of, anthropocentrism. But this is what I'm trying to get at: the mere fact that something is unique to humans doesn't make it significant or valuable - e.g. being a featherless and relatively hairless biped doesn't seem significant to me. But the fact that we're able to communicate in the way we're doing now, and the fact that we're even capable of sustaining this complex technological society is to me just a clear way in which humans are exceptional. We can look into why that is, and that to me is a very interesting question, and we might find that many of the traits that make this possible are shared in some ways with other animals, but there's just obviously the fact that no other animals come close to being able to replicate it.
Having said that, I do have the feeling that the ways in which humans are exceptional are themselves exceptional: we can consider dolphin sonar or echolocation in bats, or cultural practices like chimpanzees learing from each other how to crack nuts with stones, still it's a long way from creating a sophisticated technological civilization.