It's complicated
"Have I got this right, a standard mobile phone can transmit a strong enough signal to be picked up by a starlink satellite orbiting at say -checks Wikipedia- 1100 km??"
Just spent 20 minutes plowing through numbers, I'm mildly confused and quite likely wrong, but I think the situation might be something like. The original plan was to put the Starlink satellites at 1100km, but they later decided that lower orbits were better -- presumably to reduce latency and/or the number of signals that might be contending for service at any given time. Anyway, they currently appear to have something like 3800 satellites orbiting in multiple shells at altitudes between 520 and 570 km. They do plan to use lower orbits for at least one later group.
From a signal strength point of view, there's not that much difference between 550 and 1150 km -- 6db I think. But half the latency.
Then there's the fact that it's only 550 (or whatever) km if the satellite is directly overhead. The further it is from directly overhead, the greater the distance
Anyway, I expect that the 2 or 3 watt output from a cellphone probably can make it 500 km or so if background noise is low and there's a satellite near overhead. But I wouldn't be surprised that you really did have to hold the phone just right to make a call.
And in the case of the Ukraine, I wonder how hard it would be for Russia to jam the cell phone channels.