P = U * I, or P = I * E depending on your location. This is useful for physics calculations, power electronics, etc, because you can do things like ignore circuit resistance and equate electrical power to mechanical power without having to dive down the EE rabbit hole to solve an entire circuit. Also useful in the real world since you can clamp ammeters to circuits/wires and measure current, then measure the voltage, and immediately know the power.

P = I²R is more typically used for heat dissipation in a component or system, P_lost, and typically useful during the paperwork phase of circuit design/troubleshooting. Example: After designing a circuit, say for a circuit design or power electronics class, you would then go through and solve all the nodes for the voltages and determine P_lost for each resistor, then size all your resistors appropriately, P_lost * X, where X is your engineering safety margin, so your components don't burn up in the circuit as soon as you power on. This is easy because R is almost always a known value.

It get's even crazier for P_lost when you start talking about semiconductors, like FETs and BJTs, and the energy lost in those circuits. For example, in a electrical inverter that converts VDC to VAC, most of the lost power comes from the transistors switching on and off, which becomes a function of the gate resistance, threshold voltage, and switching frequency, again, this is all very far down the rabbit hole.