An update: I can reproduce in a VM running a slightly simplified version
of ‘hydra/berlin.scm’, with loop running:

  while true; do wget -qO/dev/null http://localhost:3000/nix-cache-info; done

to trigger ‘guix publish’ logging.

Better, I can mostly reproduce the issue with the attached config file,
then starting shepherd:

  rm -f sock && ./shepherd -s sock -c log-conf.scm -I

… monitoring heap usage:

  ./herd -s sock eval root '(gc-stats)'

… and triggering inetd service startup, which in turn triggers heap
growth:

  while : ; do echo foo> /dev/tcp/localhost/4567 ; done

Then the heap size reported by ‘gc-stats’ seems to hit a threshold above
which is stop growing, or it grows too slowly (IOW the problem is not as
easy to observe as on berlin).

That’s pretty much all I have so far.  :-/

Ludo’.