I see a solution to my problem:
su
cd /usr/share/applnk/Applications
mv -i * /usr/share/applications/kde
cd ..
rmdir Applications
It seems that "Applications" now is a dummy folder name that
is used to show only desktop files whose categories are not known.
They show up in the K Menu in Lost & Found. So no desktop files
should be in /usr/share/applnk/Applications, and in fact that
directory need not exist.
So long as they are NOT originally from
/usr/share/applnk/Applications, the files appearing in Lost & Found
can be deleted or moved to other folders using menuedit, and will
then NOT appear any more in Lost & Found. This is the correct
behaviour.
Since the menu system does not display empty folders by
default, the Lost & Found folder itself will not appear in K Menu
unless there is something left in it, or something landed there due
to some package putting a desktop file somwhere that has no category.
So, fine. I think I'm with the program now.
One rough spot I noticed: A KDE desktop file that is
(1) From one of the (legacy?) folders like
/usr/share/applnk/Development, etc., and
(2) Does not have a valid Category entry,
cannot be given a new icon. The modified desktop file will be made in
~/.local/share/applications/kde-xxx.desktop
but K Menu and kmenuedit (on next start) will ignore it.
Maybe this is the price of transition? The work around is to give
the offending desktop file a valid Category line. Then its icon
can be modified as usual.
