Overloading a breaker should cause it to trip, turning everything off. (Unless you've got a Zinsco or Federal Pacific or some other obsolete or recalled breaker box.)

Overloading a circuit (or using a long chain of extension cords) might cause the voltage to drop too low. You can measure voltage while using all your devices with tools like this: https://smile.amazon.com/Receptacle-Electrical-Klein-Tools-RT250/dp/B08QW7K1JJ/