In this scenario, is the Network-Attached Storage attached to the network (and so theoretically vulnerable)?

It seems like the only “safe” option is a PC (+storage) that never attaches to a network, but that extremely limits its usefulness.

This is correct; two of my three ZFS implementations are entirely local... the third (public-facing) covers the other twos' "limited usefulness."

Perhaps a vulnerability still exists (for one offline NAS, only): I use dedicated NICs (on each end) to direct-link my online NAS (which is otherwise local network, only, on a separate NIC), for routine backup.

Perhaps this leaves a bridge-LAN vulnerability?

But one is entirely offline, as are all its clients (dumb TVs, mostly).