Attention: Modules manufactured with DS3231 and an EEPROM memory may be for a different type of battery, maybe LIR2032 (rechargeable) instead of CR2032 (not rechargeable)!
If you are going to use the module with CR2032, you should remove the resistor or the diode, in the last case cut the PCB track.
If your module is still original, check the battery voltage with the module powered by 5V, if your battery has a voltage greater than 3.3V, check the module circuit. Or just check the circuit. I found a module with a 4.3V battery and expanded body.
Do not use an expanded body battery!