The problem was there is no shutdown in /usr/sbin and since slim complained about rights last time I set it up, it didn't occur to me to use /sbin as a user.

In this specific case I also made quite move, I confess.
The old machine was running a debian 9 (stretch). I installed the new one with ascii as minimal install and then generated a list of all installed packages on the old machine, which I used to install all of them on the ascii installation.

Worked surprisingly well, even tough I had to change the tde-trinity sources.
Anyway it's running with slim and the sudoers config. (I need to prove, if I removed the standard sudo entry and removed the normal users from the sudo group).

/usr/sbin/

is not set in the $PATH by default.

That is also true for /sbin so the normal user's PATH would not include the commands you've listed in /etc/sudoers

To include the {/usr{,/local},}/sbin directories for all users edit /etc/profile and change these lines:

if [ "`id -u`" -eq 0 ]; then
  PATH="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
else
  PATH="/usr/local/bin:/usr/bin:/bin:/usr/local/games:/usr/games"
fi
export PATH

To:

if [ "`id -u`" -eq 0 ]; then
  PATH="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
else
  PATH="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/local/games:/usr/games"
fi
export PATH

Or to include them for specific users add this line to ~/.profile:

PATH="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/local/games:/usr/games"

Be sure to place that before the lines setting PATH to include the user's private bin.

rolfie

Unfortunately the notebook is now not in my direct reach, I can't test directly (but I have the next Notebook to install lined up).
(the fix here was: install slim and make it the default login manager:

dpkg-reconfigure slim

and entries in sudoers:

# shutdown for users
%shutdown ALL=(root) NOPASSWD: /sbin/shutdown
%shutdown ALL=(root) NOPASSWD: /sbin/halt -p
%shutdown ALL=(root) NOPASSWD: /sbin/reboot

But someone posted in the Debian forum it might be even easier to fix:

/usr/sbin/

is not set in the $PATH by default.

I was about to proof that, but figured, that there is no shutdown in /usr/sbin anyway...

What I do know about is using lightdm with elogind. Another forum user already found the solution: HOWTO: lightdm (with libpam-elogind) + xfce4 (ASCII/Stable) / Documentation / Dev1 Galaxy Forum

My current solution, derived from the above link:

#!/bin/sh
# Reference: https://bgstack15.wordpress.com/2019/09/01/devuan-with-lightdm-and-xfce-will-not-let-user-reboot-or-shutdown-from-user-session/
# Startdate: 2019-08-11

# only for devuan ceres
sudo apt-get install --no-install-recommends libpolkit-backend-elogind-1-0 policykit-1 lightdm lightdm-gtk-greeter

sudo sed -i -r -e '/session\s+optional\s+pam_systemd\.so/s/systemd/elogind/;' /etc/pam.d/lightdm-greeter

My fix is to use slim, which I like better anyway, ...BUT I just learned right after implementing my fix, that slim is pretty much abandoned. Main statement is due to "not beeing fully compatible with systemd".
So question is (from a non programmer): Will it stay in Devuan? 
Or more general: Can't there be unmaintained software, which is still usefull and without objections to use? Or is there realy no such thing as a software, that is simply "finished"?

And if there is no way to keep slim alive? Is there any other login/display manager, which simply does the same in terms of shutdown/reboot by users?