Since the intention is a children's toy, I'm trying to get the price as low as possible. This display size is cheap because it's intended for grocery store price tags ;)
Flat Flex e-paper displays are available but much more expensive. Plus, the magnets in the cards which let them mate to the base take up most of the thickness. I'd have to rethink that physical interface entirely if they needed to be much thinner. My next step will be to design an actual game and then I can come back to size for a v2.
Also see his HN post: Feedback Welcome: I am developing an e-paper calendar as a consumer product (2021) https://news.ycombinator.com/item?id=26216357
It is an eink smart screen. The calendar app supports Google calendar and anything that can provide an .ics event feed. I just added a new "Picture Frame" app, though admittedly enjoying your photos on black-and-white eink is a niche taste :D
https://shop.invisible-computers.com/products/invisible-cale...
If they were thinner and wider, I suspect that an almost unlimited number of uses could open up for them.