@codinghorror, have you thought of using a different board for this project? ESP32 has everything you might need - I2C\SPI for the screen, WLAN, and deep sleep support.
As how you can do it with RPI: You can use a pi pico for timed switch functionality or one of these hats.
Maybe you can try to underclock pi0, disable all interfaces, etc to get as much battery life as possible, but I am not sure if you’d be able to get more than a week out of 12800mAh with pi0w.