I don’t know that means Bluetooth will be running when the device is off. “Specialized hardware” could mean a full Bluetooth modem on backup power, but more likely it’s means there’s a low power beacon. Would be interesting if anyone does a teardown of the Pixel 8.

For non-Pixel 8 devices, definitely not. I assume “Offline” refers to the case where your device doesn’t have WiFi/LTE, but can still use Bluetooth to communicate with devices that do.

I also couldn’t find a mention, and it definitely does not make sense (and likely isn’t even possible) to run Bluetooth without Android itself running

…which uses a crowdsourced device-locating network to help you find your lost or misplaced devices and belongings quickly – even when they’re offline.

Maybe this line is being misinterpreted?