I bought an HP in March 2020 when my job went remote and HP bricked it remotely after only 100 pages because I wouldn't sign up for their subscription program. Ended up trashing a perfectly good printer.
Luckily my library's close by and I can print there remotely.
"It's blank therefore not connected" makes as much sense as saying "my phone's screen is off, therefore not connected." If you've got a smart TV, "Off" is more akin to "Standby." If it's connected to internet you should assume it's receiving updates, the latest ad rolls, etc at all times if you haven't completely firewalled it off.
Can't speak to them utilizing open APs or mesh networking like Sidewalk but I wouldn't trust that they couldn't if they wanted. Thought I'd read up that some of Amazon's devices even use LoRa which, while low bandwidth, can cover quite some distance.