Or, how to design a simple DC-DC up-converter. The coin cell is still low voltage.

I had a couple of LED candles (I misplaced) that used a similar circuit to drive the LEd powered by what would normally be considered “dead” AA batteries for months.

This is kinda cool if you didn’t know this was possible, but dc-dc boost and buck (up and down) converters are -extremely- common these days, and not in any way remarkable.

I recently integrated one that is a total of 4mm2 that handles up to 1.5 watts for a tiny wearable sensor. It costs $US0.009 to build.

It's a Joule Thief.