Does Systemd read /etc/pm/.....?

Scripts in /etc/pm/config.d|power.d|sleep.d are ignored under systemd. Instead a systemd "unit" (service) must be created and enabled.

To restart networking after the system resumes from sleep I created the file /lib/systemd/system/root-resume.service:

[Unit]
Description=Local system resume actions
After=suspend.target

[Service]
Type=oneshot
ExecStart=/bin/systemctl restart network-manager.service

[Install]
WantedBy=suspend.target

Then I activated the service with sudo systemctl enable root-resume.service. Enabling the service creates a symbolic link for the file in /etc/systemd/system/suspend.target.wants/

Contrary to man systemd-sleep service files placed in /lib/systemd/system-sleep/ are ignored.

No, nor those in /usr/lib/pm-utils/sleep.d. But it runs all scripts (not service files) in /lib/systemd/system-sleep/ with executable bits set.

Here's an example one for calling pm-powersave, modified from /usr/lib/pm-utils/sleep.d/00powersave.

#!/bin/sh

# do not run pm-powersave on ARM during suspend; the 1.5 seconds that it takes
# to run it don't nearly compensate the potentially slightly slower suspend
# operation in low power mode
ARCH=`uname -m`

case $1 in
    pre)  [ "$ARCH" != "${ARCH#arm}" ] || pm-powersave false ;;          
    post) pm-powersave ;;
esac
exit 0

$1 is "post" on resume, "pre" otherwise. $2 in both cases contains either "suspend", "hibernate", or "hybrid-sleep".