(This should already be clear given that robots do exist, and we do call them robots, as you yourself noted, but never mind that for now.)
It’s not even about the level of mechanical or computational complexity. Automobiles have a lot of mechanical and computational complexity, but also aren’t called robots (ignoring of course self-driving cars).
Generally, it has to automate a task with some intelligence, so dishwashers qualify. It isn't a existence proof (nor did I state that).
My point is simply that we absolutely do not refer to a home dishwasher as a robot. Nor an old thermostat with a bimetallic strip and a mercury switch. Nor even a normal home PC.
I know I could google it, but I wonder washing machines originally was called an “automatic clothes washer” or something similar before it became widely adopted.