Here goes another round of findings. The link to Make a split library portable was most interesting, since it showed, that the iTunes library structure has changed from iTunes 8 to 9. So since iTunes 9 there is a new structure in place.
Thanks to Apples lack of detail in changelogs I was not aware of this change. Apple has not mentioned the change in the log nor has iTunes informed the users about it.
This KB iTunes: Understanding iTunes Media Organization explains how to update an old library. After doing that, the behavior when tagging audiobooks changed: audiobooks are indeed now moved to a separate audiobooks folder (which is just what I want and imo sane file structuring, so apple did the right thing there).
Remaining issue
What's still not working is, that files which I tag as audiobook, remove them from iTunes and then re-add - they still end up in the music section which is really stupid. Since the user tagged those files as audiobooks, the best bet would be to add those files to the audiobooks folder and have them show in the audiobooks section of iTunes.
This is imo a bug and should be fixed. The tag I mention earlier does not seem to be used by iTunes itself. I also tried again, to manually add the ITUNESMEDIATYPE tag with value "2" to no avail. Those files also showed up in the music section after re-adding them to itunes.
The thought process of apple here is beyond me. This is a bug and should be addressed. Or again others are welcome to chime in and tell me more about this process.
I have learned a lot thanks to this thread already and am really thankful for all the input. Updating the library was overdue - I just wasn't aware.