How do electrical appliances "know" to draw only a certain amount of power?

The filament has a property called resistance which limits the amount of current that can flow. A paper clip has very low resistance. All electrical appliances similarly have a certain amount of resistance, intentionally designed to keep the current flow at a particular maximum.

With an old device like a dumb heating element or incandescent lamp, it is designed with a certain resistance so that when connected to the specified voltage, it will draw the correct amount of current to dissipate the amount of power it says on the label. See Ohms Law. If you connect it to a voltage twice what it is designed for, it will take twice the current and consume 4x the power,m and probably melt.

A paper clip counts as a dumb heating element.

With a new smart device like a cellphone charger, it gets more complicated. The electronics inside may actually measure the current and temperature of the battery and adjust the input current so that the charging current is optimal, regardless of the input voltage (within limits).

Other appliances have a thermostat so they turn off when they are hot enough; your washer "knows" not to boil your underwear.

while developing an electrical appliance the manufactures considers the parameters like operating voltage, capacity of the device etc,.. according to that they develop the device. for that operating levels they design the device proprieties like resistance or impedance or required inductance or capacitance and so on

so for that design considerations we can calculate the power consumption of the device. these devices are particularly designed so they allow the current we specified ( they have particular resistance only)

so that they limit the current through them

But in case of stick a paper clip it having a small amount of resistance so that it consider as short ciircuit, that is shotest path or low resistance path for current to flow. so all amount of current prefer to flow in that path so a large amount of current flows through it (amount of current is not controlable)

Because current was limited by the device total resistance. A 100W lamp has about 144 ohm. So that it draws 0.83A ,not more or not less.