Circuit breakers are there to limit the total current carried over the wire in a circuit in order to protect the wire. That’s why they are matched to the wire size (gauge.)
Unless an appliance is defective, it will pull no more current than it needs. For example, if a toaster is rated at 900 watts, it will only pull about 7.5 amps (900w/120v) whether the wiring to the outlet it is using is protected by a 15-amp breaker, a 20-amp breaker, or a 30-amp breaker.
An appliance cord is matched to the amount of current the appliance will draw. A typical AWG 16 lamp cord will not carry a continuous load of 15 or 20 amps to match the capacity of the breaker on the outlet into which it is plugged. But in normal use, the lamp cord will carry only the 1 or 2 amps the bulb(s) in the lamp will draw, which is far below the cord's capacity.
Wayne