Are you using setDeepSleep(1) on the Pico? When not doing anything that should put the power usage down to 0.02mA - which would be around a year's life on a coin cell.
However powering LEDs will drastically increase the power usage - that SparkFun watch will spend all its time with the display powered off, only turning it on when you press the button - which might explain some of the difference in power draw you're seeing?
Do you have an oscilloscope? One thing I sometimes do is power the device via a low value resistor (1 Ohm?) and then measure the voltage drop across that resistor with an oscilloscope. You can then get a pretty good idea of when and how power is being drawn.
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