In short: how do I define a regex that matches 'iskeyword'.
My initial thought was that match(str, '\w*') would match an arbitrary number of keyword characters in str, but it really only matches to a predefined list (as confirmed by :h \w). Of course, I could manually make up a target with [], but that does not feel right. Am I missing something here?
From :h /character-classes you are looking for \k:
magic nomagic matches ~
/\k \k \k keyword character (see 'iskeyword' option)
/\K \K \K like "\k", but excluding digits
Also \w matches "word" characters (i.e. [0-9A-Za-z_]) as in opposition to "WORD" characters. The difference is explained in :h word.
\w compared to its usage when talking about things like the commands w, e, etc and whose counterpart is "WORD". The latter is dictated by the 'iskeyword' setting while \w is always the pattern @statox indicates.