Thanks for clarifying it.
The default bzImage kernel already had the network drivers needed for my setup (onboard Realtek NIC). I checked the WoL status of the ethernet adapter with ethtool. It showed:
So WoL was supported, but disabled.
Then I followed this guide to enable WoL on boot: https://wiki.archlinux.org/title/Wake-on-LAN
I created the /etc/udev/rules.d/81-wol.rules file in init.xz and init_32.xz, and added this rule:
I use ATTR{address} instead of NAME, so this rule would apply to any network interface (except loopback), regardless of the interface name.
With this rule in place I can wake up computers after a shutdown task (deploy with shutdown or capture with shutdown).
TLDR; I only needed to add an udev rule to the pre-built init.xz and init_32.xz (https://github.com/FOGProject/fos/releases/latest) to enable WoL.