Gadgetbridge is pretty well on it's way to this. They roll out support for new devices monthly it seems like. Of course there are always feature X and Y that fitbit or garmin does that it doesn't, but it's quite an impressive project. I use it with a pebble 2 HR.
I built an open source app a while back that had some similar functionality to sleep as android called "Go to Sleep". Haven't updated it for a long time, always wanted to add more things