With the lessons learned in the dailies Day 132: Horde Catapult Rigged (Blender Linked Data Complexity) and Day 133: Rigging Mechanism to Rotate Wheels, today I managed to animate the catapult.
The wheels are rotated via a single controller, connected via a “Transformation” constraint. And this controller is connected to the root bone via another Transformation constraint. To animate the pushback, I moved the root bone 0.3m Y+, and then the wheels moved automagically, due to the root -> controller -> wheels connections.