Of course they can, the UI for apps on Kindles is usually created with the web application framework, it's simple HTML, CSS and JS.
https://wiki.mobileread.com/wiki/Kin...g#Architecture
Someone did almost exactly the same as I intend to with a Kobo:
https://homey.app/en-us/blog/homey-ink/
So try telling me again that no e-ink reader can do what I'm asking for.