Okay, so after network reset the problem gets back it seems. But in a weird background draining-while-doing-nothing way. I'm not sure if it is even the same problem?
Here's what happened: yesterday I noticed the dreaded drain returned, eating 20 percent in a couple of hours of battery for making few photos. So, I did network reset again, then charged the phone to 100%. Then I didn't use it, just checked the battery level.
If you look closely you'll notice that for the first few hours background consumption is basically flat. I checked the percentage and it was the way it is shown here. Then after 10pm something happened and the battery started on its steeper way down. Here's the kicker: there's no app to account for that in battery history. There's only Siri and home screen in some periods, and nothing in the rest. I bet it is some system process that don't appear in the history as a separate entry at all.
Maybe this background drain is a separate thing, and maybe it isn't a problem at all. The phone never got warmer when it was laying down doing nothing, unlike high temp yesterday.
Currently, I'm out of ideas what to try next