Further on this:

I've also got a dist-upgraded beowulf with a no-install-recommends
installation of task-xfce-desktop, and this one is fine wrt 'w'/'last'
report for slim using consolekt, and still fine when I downgraded
consolekit to the ascii version. The newest 'slim' is fine btw.

A little bit of digging tells me that my laptop has XDG_SESSION_COOKIE
set which my beowulf VM doesn't. That difference might be enough to
steer things differently for /etc/X11/Xsession.d/90consolekit, which (by
guesswork) has a significant decision point about the session startup.
Basically, X startup only runs /usr/bin/ck-launch-session if the
variable is unset (at that time).

Someone who knows stuff might kindly pull me right, but now I'm chasing
the reason why may latop gets XDG_SESSION_COOKIE set (while my beowulf
VM doesn't)...

Ralph.