If you didn't buy that used, you probably should've complained to logitech. My master 2 runs ~1 month on a single charge, and when I see the third light blinking I usually just plug it into my laptop overnight. I've not had to deal with a dead battery in this mouse, ever.
Yeah it was new. Weird. Did you have to install any drivers to get it to power save efficiently? Because I run Linux and don't have any Logitech proprietary drivers installed.