I have had a couple of additional thoughts on the subject of breaks in prose.

Short version:  I think that using <div>s is a reasonable default position,
but it's definitely something that has to be considered on a case-by-case basis.

Long version:

Firstly, while this is slightly off-topic, I don't think that there is
normally any difference between an extra set of blank lines and a series of
asterisks.  As I recall, in days before computerized typesetting the latter
were usually a way of indicating the former in a manuscript; in print the
asterisks were swapped out for blank lines during typesetting unless the gap
would occur at the beginning or end of a page.  (I surmise that this
exception is because a gap at the beginning or end of a page could easily be
overlooked due to its continuity with the margin.)  It may not have been the
case with every text, but normally a space and a set of asterisks did not
have any difference in meaning.

Secondly, while I presume that there are cases out there that defy the
norms--every rule has its exceptions--I think that in cases such as fiction,
the original question's references to "theme" and "scene" are generally
correct:  Such breaks normally mark the transitions between separate scenes
or other sections, which is the sort of thing that we usually use some sort
of structural markup (<div>s and so on) to contain.  For example, there are
fiction authors out there who do not believe in chapters; in their works the
scene breaks are often the only available structure and are a reasonable
choice for basing a <div> structure around.  (For obvious reasons, such
books rarely have tables of contents, so no help there.)  As for authors who
use chapters, if one of them has provided further divisions within their
chapters via breaks in the text, I have no problems advocating that such
divisions be marked using <div> tags.  Again, there are presumably works
where this would not be appropriate, but it does seem to me to be a
reasonable default position.

In service,
M. Alan Thomas II