I don't see any reason for thinking that everyone's cognition is equal, let alone that all animals have the same degree of knowledge. As I said in a recent article, different species likely have different expertise (squirrels likely have more practical tree-climbing knowledge than we do), but there are also general limitations that have to do with the neural hardware or with cognitive blind spots or lack of interest.

(I have a couple of articles coming out soon on intellectual elitism that are relevant to this.)

There are two considerations that might make us wary of speaking of levels of cognition. First, there's the fad of "wokenes": it's politically incorrect to say that some types of creatures know more than others, even though it's obvious there are such inequalities.

Second, there might be what you said about computation. But that's an exception that proves the rule because computation isn't the same as knowledge, precisely because computing doesn't require understanding. Computers compute results without understanding a single one of their symbols.

Cognition varies, then, because cognition requires understanding which is partly subjective, and subjects vary in their implicit interests, purposes, lifestyles, existential missions, and so on.