How can I measure my smartphone transmitted power?
How can I measure my smartphone transmitted power?

You can't.

At least not in a very meaningful way. I mean, using an SDR receiver you can get an indication of the frequency your phone is using and when it is transmitting but that's about it.

It is in no way an accurate way to measure the real output power of the phone as the SDR's input and phone's antenna output aren't coupled properly (you would need to use matching networks and an RF cable to prevent power from "escaping"). Also the phone will transmit in short "bursts" of power which is difficult to detect for an SDR.

To measure the real output power of a phone you need a stack of equipment worth much more than a couple of hundred thousand $. And then you can only measure if you manage to get the phone in some kind of testmode (like used during manufacturing). If not you will need some equipment to emulate a base station, that's another couple of hundred thousand $.

Anyway, how is the output power important? Your phone needs to fulfill certain requirements to pass qualification tests. That sets the maximum output power and that is what it will be. Usually it's a couple of Watt.