Can a household device limit consumption to avoid tripping circuit breaker?
No there's no easy way to do limiting in the way described at the end of the question. Some electric central heating equipment has exactly that feature, but then a centrally placed current sensor is used to sense total current used in the house. That information is simply unavailable to a stand alone appliance.

There is no way for an appliance to know how much current other appliances on the same circuit breaker are using, unless it has some other source of information than simply the voltage fluctuations on the line.