On modern FaceID phones you need to hold the power and down volume key to bring up the Reset/PowerOff and cancel. Just clicking multiple times will bring up wallet, siri, or do nothing.
On my iPhone 13, just now, I rapidly clicked the power button 5x.
The phone immediately made a loud sound and put up a screen that said "Emergency SOS". There was an option to "cancel" it, but I assume that the phone would have contacted 911 in short order unless I quickly cancelled.
So the correct description is probably "it depends".
In Settings go to Emergency SOS. Uncheck Auto Call
You also risk the accidental activation of an SOS call.
Yes this is kinda buried and not clear at all that this function also disables FaceID but it does.