Language is not some inherent property of the Universe; it is an evolved behavior in humans. We can study how humans perform language; and when we do, we find the syntax/semantics distinction to be naturally occurring in humans. For instance, in my example, a native English speaker will find the second sentence "awkward" in a way that they do not for the first sentence. Similarly, a native English speaker will extract a clear meaning from the second sentence in a way that they would not from the first.
It is conceivable that there is some other language (eg. not natural human language) which does not have a syntax/semantics distinction, but that hypothetical language is not what linguistics studies.
.....Which is an effect of the first satisfying first order approximations while failing higher order rules, while the latter is merely an unusual sentence and so requires more effort to parse because it falls off the "fast path". (It also arguably fails to encode embedded cultural messages present in word choice -- a second consideration for why it feels "awkward": it's valid English, but not my tribe's English.)
You haven't pointed out how semantics is anything but higher order syntax -- merely outlined the way in which higher order syntax interacts with our perception.
I agree that there's a difference between the two sentences -- I disagree that it's because they're different fields of study instead of different edge cases of the same underlying notion of parsing syntax. (I especially disagree that the way forward on teaching machines language involves that distinction.)
I would appreciate you referring me to references on the semantic/syntax divide being "natural", though.
It is conceivable that there is some other language (eg. not natural human language) which does not have a syntax/semantics distinction, but that hypothetical language is not what linguistics studies.