UPDATE:
It took some time for me to figure out how to find the article from webarchive, since some links and the search function does not work there.
While still not quite satisfying, these do provide additional details.
Part 1: https://web.archive.org/web/20201112011803/http://archive.wizards.com/default.asp?x=dnd/rg/20070327a
Part 2: https://web.archive.org/web/20161031215249/http://archive.wizards.com/default.asp?x=dnd/rg/20070403a
Part 3: https://web.archive.org/web/20171108150341/http://archive.wizards.com/default.asp?x=dnd/rg/20070410a
So the conclusion is:
- Unarmed Strike/Unarmed Attack is neither manufactured weapon nor natural weapon, so the rules like "can be used as a secondary attack" do not apply to them. The best you can do is to use it as an offhand attack.
- For the weapon enhancement purpose (and for that purpose only), the Unarmed Strike/Unarmed Attack is always considered as a natural weapon, if you are not a monk.
- On the other hand, a monk can take this as both a natural weapon and a manufactured weapon. Those articles keep using examples of taking unarmed strikes as off-hand attack in TWF but never explain if it can take as a secondary attack in the form of natural weapon if the character is a monk, leaving the question unanswered.
(It seems, though, that the unarmed strike cannot be used as a secondary attack, even for a monk, and is always considered as manufactured weapon in this case scenario. But the author never points this out in those articles.)