How to reduce voltage from shift register to ESP32 MISO pin?
While the datasheet is not clear on what the absolute maximum ratings for the IO's are, I am certain that it's 3.6V. Usually "+0.3V" means that the inputs are protected with a diode that turns on at Vdd+0.3V. So this means don't tie Qh directly to the port of the ESP32, it could burn out the diode. 

  

Source: https://www.espressif.com/sites/default/files/documentation/esp32-wroom-32_datasheet_en.pdf

The resistor divider isn't working because it's not dividing the output voltage from Qh, it needs to look like this:

  

The Voltage output specs for the SN74HC165 are Voh = 5.99V and Vol = 0.1V, after the resistor divider this would be 2.7V for Voh and 0.045V for Vol, using a resistor divider is compatible range of the ESP32's Vih of 2.475V and Vil of 0.825