In the web portal when you hover over the sleep details timeline it shows you the specific times but in the mobile app (android at least) you can't interact with it. It also doesn't even rotate to portrait so you can see more detail.
It would be great if you could interact with the plot similar to the activity heart rate, cadence, etc plots - but at a minimum it would be nice if tapping on a segment showed the start and end times of that segment.
Fitbit won't show me my old sleep data since I unpaired my old device, but if I recall correctly it did let you tap/drag across the sleep timeline to show specific times (I think it also let you rotate to portrait with the chart)