Natural sleep has a cap on length - 10 hours.
If you have no insomnia trait, you can retry sleeping after waking up - it can often be successful. If you have the insomnia trait, sleep problems are a feature, not a bug.
A full-length sleep regenerates 240 fatigue. Tired status starts at 195 or so.
1 fatigue is gained per 5 minutes, so 12 per hour, meaning it should be 20 hours (with no traits) per full length sleep. 20 hours to get fatigued back to pre-sleep point, not to get “tired” status.
Sleeping until “well rested” gives a small bonus on top of that - 25 points, so 2 hours.