With an e-ink device you could create something that only needs to be recharged 1-2 times a year, or that is passively charged off your WiFi.
I had no idea this is possible. Is there a name for power-over-wifi?
Yes, the name for power over wifi is power over wifi (or PoWiFi).
But doesn't look like it's used at all in anything and uses a special "PoWiFi router"(?)
https://modernmobile.cs.washington.edu/docs/powifi.pdf
With an e-ink device you could create something that only needs to be recharged 1-2 times a year, or that is passively charged off your WiFi.