We just need to backronym the shortcut to make somewhat redundant name of "network attached server"

Just call it a home server.

I don't mind too much that a NAS runs file-sharing-oriented software as a bonus feature - if it can run Samba why can't it run Immich? But when you start using it for compute tasks it's not a storage box any more by definition. And that would be a more advanced extra feature whereas the basic functionality of a storage box is always storage.