Your ampmeter will smooth out current draw of a measurement of about 0.25 to 0.5 seconds. So you're measuring the average, not the peaks.
My measurement indicates "about 800mA". This could very well be 600 or 1000mA. THAT is not important. What IS important is that you say "about 120mA" and the difference with the "about 800mA" that I'm measuring. I'd like to know if you've just got enough capacity on your 3V line to last the packet transmit, or that my ESP is drawing much more than yours.
(On the backburner is using the 3V line as a voltage reference. With 1ms droop-periods, that would not be acceptable.... ).