Pullup resistor operation between the ESP32 and a Bus MCU
The pull-up wiring is correct, but assuming you have 3.3V available on the circuit for the power supply of the ESP, I would pull the pins to 3.3V to avoid damaging the ESP pins. Afterwards you don't have to worry about the output type since you are already in the safe limits.

According to the datasheet of ESP8266, the maximum I/O current is 12mA, so it should easily pull the line low with a 10k pull-up resistance.