At what outdoor temperature is it recommended to switch thermostat to Emergency heat setting on a heat pump?

It really depends upon the brand and the SEER capability of the unit.
You need to do a electric energy calculation to see when the break even point between electrical resistance heat and heat pump.

There is heat available in the air down to zero but the cost of recovery by heat pump gets expensive. You are also running the compressor more which is more wear and tear and shorter compressor life.

If you just want to guess pick any number.
If you want to do it correctly do the math.