Most of those devices do in fact sleep most of the time. It's like your phone: it may last 2-3 days standby with the screen off and nothing running but if you're running a heavy CPU/GPU load it'll chew through the battery in maybe 2-3 hours or even less pretty easily. A smart watch pretty much never runs at full power other than the maybe 5 seconds when you look at it and the display lights up and there's some animations going. Otherwise it's pretty much just polling the sensors every now and then, and going right back to sleep.
It's not hibernation or even conventional S3 where everything turns off, it's more like S2idle on modern laptops. It's still on but it does power off a lot of the peripherals and drop the clock to near nothing, but it's ready to wake up quickly on timers and interrupts, and it can handle some networking and go right back to low power within a millisecond. And similarly to PCs, those chips change speed based on demand. No point running at 800MHz if it only needs 50 MHz to read sensors every now and then and keep the Bluetooth connection alive.
Even Arduinos go from a few mA to a few μA when in sleep mode.