200 W at the heater.
When the power meter was being fed with from the rectifier, the RMS voltage wasn't being measured correctly. If the mains voltage was 125 V, the RMS current when half-wave rectified would have been about 88 V.
Some hair dryers have a low power setting that has a diode in series, so power meters like that are expected to work correctly with loads like that. Having the rectifier after the power meter is the way to take the readings.
I would expect readings to be about:-
Voltage 125 V
Current 2.3 A
Power 202 W (as you already told us)
Power factor 0.71
Without the rectifier I would expect
Voltage 125 V
Current 3.3 A
Power 414 W (as you already told us)
Power factor 1.0
If you are getting those readings, they would be consistent with the rectifier working perfectly. The readings with the power meter after the rectifier are just an anomaly from using the power meter in a way that it's not intended to be used.