I just found that when I use 4K super-35mm recording on A7rii (newest 4.0 firmware), the face detection function was forced OFF. And the message shown on the screen is 'This function is not supported during 4K.'
I searched online and found one YouTube video, and the solution is to change the 4K HDMI output set to '30p HDMI only or 24p HDMI only' when connect to an outside recorder/monitor, then face detection will be ON. I tried it with my 4K TV and it worked.
However, when A7rii was disconnected from the 4K TV, the A7rii face detection function was forced OFF again. I confirmed with the Vlogger, he is using A7Sii and he could get face detection ON always with/without outsider recorder, as long as the 4K HDMI output is set to '30p/24p'. It turned out that on A7Sii, this option is always adjustable with or without outside monitor/recorder connected. But on A7rii, this option is grey and not adjustable unless it is connected to an outside HDMI equipment.
It seems someone asked similar question on Sony community but the reply is just copied content from manual and not helpful at all.