Can I use a Raspberry Pi for the video

I can’t understand why others aren’t doing this - but how would I connect to the Apple TV unit?

Install raspbian on the Pi, connect your USB drive, and then setup SMB sharing in raspbian.

If you don’t know Linux is stop here and look at a more consumer based solution such as a NAS or a windows PC.

I guess you can use a cheap NUC too?

Yep. As long as the device isn’t doing anything else other than serving files that would work as well.