Your on /hn/ and ¡¿don't?! have an entirely-local subnet, offline, for your NAS?

...with a hint of sarcasm, but the percentage is definitely a non-zero number.

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).

Your NAS is not critical. The plan if your NAS gets compromised is to say "dang" and wipe it and re-download all your movies or whatever. You can connect that to the internet.

Stuff like your town's water, transportation, and medical infrastructure and employee and student data are critical. Your car's drivetrain and safety features are critical. Your home's HVAC can be critical in certain times of year. These things should not be connected to the Internet.