Generally most sleep tracking products use actigraphy (measurements of your movement) to track sleep. Pebble partnered with researchers at Stanford back in the day to produce an algorithm for our operating system, which worked quite well and is now open source!

You can read the code and see how the sleep tracking algorithm works here - https://github.com/coredevices/PebbleOS/blob/main/src%2Ffw%2...

I own the Pebble 2 Duo and the answer is "almost none". It basically just tells you how long you were still/not moving much in the evening, as you'd expect. It's a pretty good proxy for what time you went to bed and got up, and that's about it. It can't actually tell if you're asleep.

There are also (currently) no sleep metrics on app itself; you can only see them on the watch, which doesn't show much besides the sleep duration and an abstract representation showing where you might have woken up in the night.