What is the impedance of a multi-tap impedance matching transformer when all taps are used at the same time?
To produce the same power in a 4 ohm load as an 8 ohm load requires that the 8 ohm load receives an RMS voltage (or DC voltage for resistors) that is \$\sqrt2\$ as high as the 4 ohm load.

For instance with 4 volts on the 4 ohm load, a power of 4 watts is produced and, to produce 4 watts in an 8 ohm load requires 5.657 volts.

This relationship dictates the relative turn ratios for the load windings i.e. if the 4 ohm load connects to a 10 turn winding then the 8 ohm load connects to a 14 turn winding. It's approximately 1.4142 x higher but near enough.

So given this relationship, it can be expected that using an ideal transformer, both loads will produce identical power outputs.

If the 8 ohm load produces an impedance of 4 kohm at the primary then so does the 4 ohm load on its winding and, if both are connected simultaneously then the load at the primary would be 2 kohm.