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).
Just a heads up, there's been a fair number of bugs and issues around sleep mode. Most of the problem seems to be in software and the situation has improved, but you might want to look into the exact state of things.
I'm working on an ESP32-based product that doesn't use sleep mode, but I've noticed people reporting issues about sleep mode on GitHub and in forums.
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).