There are other microcontrollers capable of driving an eink display that consume a lot less power out-of-the-box. Eg: atmega328 (~5 μA deep sleep, ~10mA running)

If you want wifi, then ESP is probably a good and cheap fit. A wemos d1 in deep sleep doesn't consume _that_ much power (~80 μA), unfortunately it does draw a lot when booting (~200mA).