Battery powered (e-ink) display?

If you want control what it does there is not much standard stuff is available, though I did see something lately, don’t know where. You might want to google for that.

Home built does not have to look bad though, see:

A clock would require each minute updates, reducing battery life. Also color is quite intensive on the refresh, and partial refresh is not supported. So I’d go for a BW (two color) disply that supports partial refresh. Note that you need to buy a dedicated lipo battery because almost USB powerbanks switch off when the display sleeps and won’t come back on.