[stumped]

Ok, your problem will be finding an app with a compatible control scheme. Easier if your android tv will accept an air mouse via a usb dongle.
If all you want is a display ,could u use a photos app to browse book cover pictures?
You can get all the cover pictures out of calibre easily enough, copy them to a folder in , say, Google drive, then try to view that.

Having said that, my android tv based Nvidia shield TV lacks the abilly to see Google photos. It can only scan for and display pictures on its own local storage.

You can in fact copy a whole calibre library into g drive if you have enough space. The TV should see it via cloud so will not have to locally store it

I don't think getting android tv to eand emails with attachments will be very doable though, so you may have to fulfill their choices by some other method

Android TV, and kindle / Amazon cloud don't really play nice together.

You could try sideloading kindle for Android app, but I would not be optimistic.

Moon reader may sideload more easily and it has its own bookshelves display feature