I own 3 EVs. Two of those, from 2012 and 2014, were built with 3G modems, and fully lost connectivity in 2022 when the 3G networks were turned down. Nothing changed, not even an error message inside the car, except that trying to connect to them with their apps now fails. They're still totally functional cars. The failure mode on both appears to have been "guess I don't have service, I'll sleep the modem." Bluetooth still works, but even if that failed one of them has a functional CD player!

My newer EV that came with LTE connectivity will also fully work without network connectivity, except for the apps and remote updates. You can turn off the built-in cell connectivity via the head unit menus, and if you're especially paranoid, you can pull the fuse on the modem (and I've done it!). When it doesn't have a network connection it too operates just like a normal car.

There's a lot of fear around EVs being "software on wheels" based on a few manufacturers making non-remote features that depend on remote connectivity and botching updates or requiring subscriptions, and I agree that all is super problematic both from a privacy perspective and point-of-failure reason. But there's absolutely nothing intrinsic to the core design of EVs that demands that they're connected to the network.