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.
This isn't even a joke. In uni, my professor had us peer review each others' argumentative papers and create an American Chopper meme summarizing the papers.
First pane thesis, second pane predicting common criticism/objection, third pane rebutting, fourth and fifth further evidence and conclusion.