It’s rechargeable battery powered. The front derailleur takes more power to do its thing, so when power is low, the system automatically drops you into the small chainring and disables the front shifting. The idea is that this will get you home relatively comfortably since you still have the full range of your cassette.
Still…a full charge lasts me many weeks of riding, and I ride quite a lot…about 10-15 hours a week.
Also, I’m describing shimano’s version of electronic shifting, where everything is connected physically via electric cables, so there’s one battery (mine is hidden in the seatpost). Sram’s offering has every component (derailleurs, shifters) communicating wirelessly and every piece has its own battery.