I did some investigation of the Pico Micropython sleep modes. (see thread below)
In the end I found the best way to save power with the Pico is to power if off via something like the Makerverse Nano Timer. The software sleep modes are not as good as the Arduino & ESP32.
All the best.
Jim
PS btw my previous post about a current shunt and measuring the voltages will not work very well. The differences are too small to be accurate enough for the Pico & Arduino ADC’s. It would need an Op Amp to see the small changes and produce a corresponding amplified voltage output. I tested the Pico and Arduino on a simple circuit. The Arduino values were more stable and varied by about 3 or 4 for the same pin. But for a 50mA current the ADC values were too close to be reliable for calculating current.