If using the Raspberry Pi 5 I wouldn't go for a battery-powered solution because it's pretty power hungry. But you can run this screen just fine off of a Raspberry Pi Zero, or ideally a microcontroller if you want basically no power draw while it's sleeping. I was just lazy.

The similar project I'm working on is looking like it'll get about a year of battery life with a typical 18650, the 5.65" version of the display and run off an ESP (refreshed once a day).