Now that said, the idea of comparing programming languages with natural languages or even constructed languages seems very strange to me. Natural languages are tools for thought, expression and communication. Programming languages are tools for, well, programming. Even the relationship between the grammar of a PL and the grammar of a human language is distant (we often intuitively think of identifiers as similar to nouns and verbs in human languages, but in fact all identifiers are equivalent to proper nouns in human languages, and the actual equivalents of nouns and verbs are stuff like block openers, significant white space, function application, maybe the keywords).
It is a well-known fact already that humans can only naturally learn human languages, which have a specific kind of grammar. Even some clumsy attempts at standardizing human language end up introducing un-natural grammar that children can't pick up until later in school when it is drilled into them. It would have been truly surprising to find out that we can use our natural language capacity for something as alien as a PL.
One issue in the study is what a reasonable comparison is. Our ancestors would have talked about "there is a lion over there" and such mundane things all the time, so we shouldn't be surprised if we're just "nexting" those kinds of things with a specialized circuit.
Obviously that doesn't exist for coding, but the question is whether there is natural language that can't be nexted. I'm thinking of James Joyce's Ulysees or Shakespeare type stuff. It's weird even for the native reader. Does that activate the math network?
Also, isn't that a better analogy for how you program machines? You're telling the computer what to do in a language that isn't assembler, and doesn't have the same machine model as your coding language, with a heavy dependence on shorthands established only in the context you created (by writing functions, classes, etc). I thought the reason why a lot of people find it hard to read code is because you're inherently doing something awkward, translation.
I've been learning a new language as well, with the wrinkle that it's quite closely related to one I already speak. Mandarin is lovely, it makes me wonder why there are languages where the verbs and nouns are changed. It also means you can jump into saying useful things pretty fast, you are just restricted by vocabulary. WRT coding, this is similar. Coding languages tend to have very few things you must know (except C++ lol) to get started, but with a lot of reading libs necessary to do anything in a given domain.