I have an HP wifi printer, 5820 I think. I haven't signed in to HP, haven't connected the printer to cloud.

Same for anything else. I don't see the whole "oh you need firmware update to improve the product". 90% of the time it just works.

So what happens if the fridge isn't given internet access ? Or washing machine?

> I haven't signed in to HP, haven't connected the printer to cloud.

HP fixed a remote exploit a few years back. Theoretically someone could use your local wifi printer to install a persistent backdoor on your network. In practice HP uses updates to patch leaks in their cartridge protection (the most complicated tech in the printers). And accidentally sometimes bricks printers...

Nothing, they just work as intended. I bought a Fujitsu A/C that supposedly required registering through some app. Never connected it, and I removed the wifi kit at installation. Works like a charm no problem whatsoever.