"I was concerned about the possibility of e-ink burn-in"
Happily, e-ink displays don't suffer from burn-in.
replies(1):
Happily, e-ink displays don't suffer from burn-in.
Can't say if it is due to burn-in but some manufacturers do recommend refreshing the display image periodically like every 24 hours [1].
See precautions #4
https://www.waveshare.com/wiki/4.2inch_e-Paper_Module_(B)_Ma...