Crystal dry uses a heat exchanger for drying, so I guess that is what they are referring to. I guess you could try to claim that only the way HVAC's move heat around qualifies for being called a heat pump, not any other way of moving it should count right?

Here is what I got from Gemini:

Bosch does not refer to their dishwashers as having a "heat pump" in the same way the term is used for HVAC systems; rather, the part is often called a circulation motor and heating assembly or a combined "heater/pump" unit by users and repair sites. Bosch dishwashers use a flow-through water heater (a type of resistive element) to heat the water and a different, non-refrigerant-based system for drying. How the Bosch System Works

Water Heating: All Bosch dishwashers use a flow-through water heater, which is a heating element integrated with the circulation pump. This system rapidly increases the water temperature to the required level. It uses electrical resistance, not the reverse-refrigeration cycle of a true heat pump.

Drying: Bosch dishwashers (especially the higher-end models with features like CrystalDry) typically do not use a separate heating element for drying. Instead, they rely on a process involving a stainless steel tub and a heat exchanger or a mineral-based drying technology (like Zeolith for CrystalDry) to condense moisture and wick it away from the dishes. This is an energy-efficient method of moisture removal, not active heat generation for drying.