Do Thirdreality smart plugs need to be turned on to act as a Zigbee repeater?

I explained that I completely understand that it works (after pairing) by just plugging it in. It does not have to be turned on, just plugged in. Read the quote from AI again, it plainly states that it needs to be plugged in AND turned on to act as a repeater. It is obviously wrong.

Let me try again, the incorrect info from ChatGPT, which is what prompted this thread: