How would superconducting circuits save a lot of power in a small electric car?
They wouldn't. To address the two areas you mention:
Wiring
The wiring in electric cars is definitely an area of loss, but it's not that big a deal. The Kia Niro I recently drove did about 14kWh/100km on the open road, so roughly 15kW to cruise at highway speeds. With a 356V battery bus, that works out at around 40A battery current. At city speeds it would be closer to 10A.
At a rough estimate the battery cables are about 6mm diameter copper, so 28mm2, which has a resistance of 0.0005ohm/m. If the cables are around 4m (there and return) then that is 0.002ohms of resistance. The losses on that at 40A are 3.2W, so represent around 0.02% loss in efficiency.
As you can see that is not exactly a big issue and changing to superconductors is not going to give you any noticeable increase in range.
There might be a secondary benefit if the superconducting cables can be lighter, but this would depend entirely on the material properties and be marginal at best (unless it is a truly magical new material).
Motor
In superconductor based motors, the superconductors is used in the rotor as an extremely high strength permanent magnet. Having a stronger magnet does potentially increase power density of the motor, but the gains are not that impressive for the overall system. Note that you still need copper windings for the stator, so superconductors cannot make the motor 100% electrically efficient with current materials we know about.
For example, the Tesla Model S motor weighs about 35kg, but the entire vehicle is 2000kg. Even if the use of superconductors halved the weight of the motor, this is a trival change in the overall vehicle weight and will offer almost no improvement in range.