You completely fail to understand Gödel's incompleteness theorems and the halting problem if you think they are evidence of something humans can do that machines can not. It makes the discussion rather pointless if you lack that fundamental understanding of the subject.
The same thing goes for image generation. Every picture is new, but it's a combination of the pictures it founds. It does not learn about things like perspectives, values, forms, anatomy,... the way an artist does which are the proper dimensions of drawing.
> that humans somehow exceed the Turing computable
Already done by Gödel's incompleteness theorems[0] and the halting problem[1]. Meaning that we can do some stuff that no algorithm can do.
[0]: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
[1]: https://en.wikipedia.org/wiki/Halting_problem