I've been wanting something like this for ages. Even as a small-scale secondary monitor, it'd be great to toss static text like tickets or APIs onto an eink display.
Oh yes! At least Kobo readers are Linux and you can SSH in. You could even install another distro I believe. Some ugly hack could be rendering the display content on your machine and just sent the image over.
https://github.com/koreader/koreader uses Lua so maybe one could add some bidirectional or at least PC->Reader flow of data.
edit: VNC! https://www.joachim-breitner.de/blog/660-Using_my_Kobo_eBook...