Door locks come in two typical styles. The first allows simply releases the door to allow you entry, usually a one time admittance per release. The second unlocks the door lock itself (like a car door), most of these are actually a motor. With a motor, two diodes and two limit switches you set the motor up to turn off when the limit switch is tripped thereby preventing it from going into a stall and gulping current.
View attachment 75848
That would not require a complicated stepper motor driver.
Unfortunately, any of the three options will most likely drain a CR2032 in a few actuations. They typically have a 240mA-Hr capacity. The 3V motors I quickly looked at draw 100mA. Granted it will only fire for a few seconds, but you cannot draw all of the 240mA-Hr from the battery for just the actuator. It must also supply the micro and other circuitry. All of the stuff has a minimum voltage requirement, and where it is starting at 3V, there isn't a lot of headroom left for the battery voltage to droop before the circuit shutdowns for low voltage.
Is there any way of getting source with more mA-Hr capacity or possibly a second source that could drive or recharge the power source for the unlatch mechanism, perhaps solar recharge?
FYI. Even AA batteries offer 2100mAHr capacity. Almost 10x the CR2032. All Electronics even has a 3.6V AA 2400mAHr battery that might work really well.
https://www.allelectronics.com/make-a-store/item/LBAT-124/3.6V-AA-SIZE-BATTERY-W/LEADS/1.html