Earlier quoted context omitted.
Makes sense since you're in the netherlands, euro appliances generally get fed cold water and warm it internally, the 2kW peaks would be when it needs to warm up the cold water. The dryer has to warm air up pretty continuously to dry the contents. At 500W I assume it's a heat pump? (IIRC condensers are usually around or above 1kW)
Ah yes, the dish and laundry washers are indeed not “hot fill”, that is hard to find here indeed. The dryer is a heat pump yes, some years ago it was the most energy efficient one we could find. (But I guess it runs longer, relying more on tumbling than heat, and wears out cloth faster).
Also, I wonder why compressors in heatpumps are not multi-speed (basically energy consumption can be modulated). If you are an expert please let me know I'd love to talk more.