Ah, I missed the part about series capacitor, was not sure what "crude capacitor power supply" referred to.
The entire point of the capacitor instead of a dropping resistor is to use "lossless impedance" instead of resistance, to drop voltage.
So the capacitor is of a value to insert significant impedance in series. That means it is "acting like a capacitor" (rather than being large enough that it is more like a short to the 50 Hz) and that characteristic will be the main thing presented to the power line as a load.
Capacitors have the current "leading" the voltage, inductors have it "lagging". So the capacitive power factor of the lamp can be helpful, since most loads on the power line are inductive. It cancels out a small portion of that.
Essentially, none of the voltage drop across the capacitor "counts" when figuring power used. Your power meter is probably correct (to the degree that is properly made and calibrated).
The lumens depends on the efficiency of the LEDs, which varies wildly depending on the LED.