Keysight 34450A
I have no experience with such high speed multimeter. But “190 readings/sec” is much slower then I run my power profiler. So, not sure, if that value fits the reality. A simple Nordic Power Profiler Kit II is quite inexpensive (around 100 Euro). There are a couple of power charts of the nRF9160 in the web, I also published some one, see zephyr-coaps-client / power-consumption
Would that be PSM sleep?
The modem has several function to save energy (mainly by switching between the 3 states faster). If you switch the modem off/on (CFUN=0/CFUN=1) the switching on takes some more energy. If you network supports PSM, then the device will be able to enter the sleepmode and wakeup faster (and with less energy). In general, people report, that the difference is quite large. In my own experience with the nRF9160 both works very close to each other.
If you want to know more about the “state” the modem is actually using, there are events which indicates RRC active, RRC ide, sleeping on and sleeping off.