do some motor evaluation. a stepper is not very efficent in use of power.
you trade power for function.
forget all the false information about steppers using more power when no moving. your APPLICATON turns the power OFF. so your application drives the math, not the other way around.
a smaller DC gear motor would run longer, at less power, but at higher efficiencies.
also, if your door is balanced, your power needs are less.
lasty, use an RF transmitter, 433 or some such to send signals. WiFi, although more informative, is much more costly in power.
my last question... if you ran the motor during the bright day, lifted a weight, then at the prescribed hour (not by light), the very low power solenoid, releases the weight.... is it more effieient to use the electricty directly or charge the battery ?
as a note, I would have thought the chickens would go in at dusk, not just because it was cloudy.....