pls delete

 

I would change the resistor to a 10K otherwise should work OK.

 

The ESP32 has a RTC, research deep sleep, it consumes 10 uA.

 

Its that the same spec for the ESP-32Cam?
From what I read the Cam version says 6 ma
in deep sleep.

 

pls delete

 

Check the voltage on the gate of the mosfet when the DS3231 is low with the micro connected to the drain.

 

In the last photo I don't see the gate connected to the DS3231.

 

Are you using the SQW output?

 

pls delete

 

the INT/SQW output is an alarm/interrupt/aquarewave output, I’m not certain that I can output a steady signal to hold your MOSFET on.

DS3231