I've had a look at a few teardowns but can't find another battery. My 'phone copes with the battery being removed while in offline mode so there's power somewhere.

But they probably do have enough power somewhere to silently turn themselves on, say briefly, according to some schedule or event. Not saying it's being done, but it could be done.

Where? No other components store power in any way. There's a few small capacitors lying around, but they're so small that you could never power anything from them. If something like this existed, people would have noticed a long, long time ago.