I looked in the default task manager plasmoid (the one with text labels) in /usr/share/plasma/plasmoids/org.kde.plasma.taskmanager/, as well in the Icons-Only Task Manager in /run/current-system/sw/share/plasma/plasmoids/org.kde.plasma.icontasks/. The later only contains a small metadata.json file and there’s no way to tell how to make it makes the task manager only show icons.
I want to edit the task manager plasmoid with my own changes as well as showing only icons.