this is much more interesting than an e-paper device; it's a memory-in-pixel lcd device, which means 100 times better refresh rate and 1000 times better power consumption than e-paper. the lcd in question (ls027b7dh01, i assume, though that information is missing from the web pages) is supposed to run on 175μW at 20fps, so you can get a full usable computer system in submilliwatt territory, so the 2.2 kilojoules in a cr2032 can power it for weeks
however, i think that, as a low-power device, this is probably fatally flawed. the rp2040 dooms it; the rp2040 lacks a reasonable deep-sleep mode; its lowest-power mode is nearly a milliwatt, so it will drain the battery flat when it's not being used
also it's unclear, in this design, how much the rp2040 can do without powering up the pi zero, which is a humongous power hog, using over 1000 milliwatts. so instead of weeks of active use from a cr2032 (and months of standby if you use a low-power micro instead of an rp2040) you get hours
what's the point of using a super expensive memory-in-pixel lcd to get the display power consumption down from e-paper's 10-100 milliwatts into submilliwatt territory if you're just going to burn a thousand milliwatts in a raspberry pi? just use a conventional lcd then, maybe one with nice 24-bit color. old nokia lcds will run on a milliwatt
maybe an esp32 would be a better middle ground if you aren't willing to go all the way to an ambiq apollo3 or something, which can (hypothetically) give you submilliwatt power consumption with workstation-class performance, as long as you don't need virtual memory; you probably want an esp32 or equivalent in there anyway for wi-fi
usb-c is a great way to be able to hook up a full-size external keyboard, but speaking usb-c to a keyboard is also probably beyond the capabilities of the rp2040, and so would also need to power up the giant power hog pi zero