If the OP wants to make something with the advantages of an e-ink display with the advantages of using Linux my thinking is the same as salamanderjuice's; get a Pi (e.g., the Zero W with headers) and connect it to an e-ink display. A google search brought up lots of hits; I started searching for raspberry pi e ink and it had lots of hits for raspberry pi e ink calendar.
But the Pi will need to be connected to power; for a battery powered setup the ESP32 is a common choice. You could use micropython on the ESP32, or C, etc. I don't know if there's code available for using micropython and an e-ink display, but ferreting around on github might yield something.
For a nice case, if there isn't one already available (and you don't have a 3d printer) you could design your own and then work with someone in your area who takes work; e.g. see
https://www.prusaprinters.org/world .