I have a very similar setup like you. A NUC is providing NAS functionality and is running 24/7. An AppleTV is connected to the projector and has all the apps I need for consuming media (Jellyfin, Netflix, etc.). The NAS is running OG Debian with SMB, Jellyfin and even NFS for easy access.
The NUC provides additional features like synching and a few other things.
Why the AppleTV? Because I had Raspis, FireTVs, PCs, and whatnot connected to the projector and the AppleTV is hands down the most convenient one. The UI is super reduced and simple. The remote works. You can get just about every app you might need. And maintainance is basically zero.