What is my simulation problem?

Coupling constraints are supported by CalculiX but not yet available in PrePoMax. They can be added via the Keyword Editor though: RBE3 integration in PrepoMax (Kinematic & Distributing Coupling)

However, I wouldn’t use them here. Try one of the workarounds proposed above. You can even apply a displacement boundary condition to the whole surface of a plate but this may interfere with contact. So maybe you could add a small extrusion to push the plate. Or push it by its edge. But most importantly, make sure that it’s stiff enough (ideally or almost ideally rigid) and meshed with enough elements.