Cell phones, even now, can't be doing
that much background processing unknownst to us, because they are connected to a battery, battery life is a
big deal in a highly competitive industry, and we'd all notice if they drained very quickly.
ISTR there are documented instances of law enforcement and/or intelligence doing that sort of thing to phones, and the battery drain causing it to get noticed.
Hooking it up to an outlet is a legit different thing.
If battery tech or power reduction tech progresses sufficiently, including just by continuing on its current curve (most power reduction rather than battery tech), cell phones will rise to the same level of concerning.
(Cell phones of course leak location data full time, and some similar things like that. I'm not saying the current cell situation is awesome either. Only that there is a legit reason to be more concerned about gear hooked up to actual power lines than portable gear.)