I'm able to replicate this somewhat using a sleeping mask, but I find most of them pretty uncomfortable; I like to sleep on my side, and that doesn't work terribly well when something's on my face.
Full disclosure here of course, I work an evening shift (12pm-11pm) so I'm used to going to sleep much later in the evening. Even still, I often found difficulty falling asleep due to light bleed from the lights around my apartment, and I feel like this contributed to my sleeping issues more than the sunlight in the morning, which my body's clock seems to have adjusted to on its own. (I still naturally wake up around 10-11am even without blackout curtains.)
Sleeping masks did not help me too, so I got thick blackout curtains for my next flat, and the first effect was that I suddenly had vivid dreams again regularly, which I only had occasionally in the years before. I am considerably more alert during the day now. In retrospect I indeed must have felt constantly slightly tired for years during the day, after sleeping in such rooms.
It is possibly dangerous to sleep in even slightly light rooms. The lowered levels of melatonin are correlated to several bad illnesses (just look it up). I push my SO who still sleeps in a too bright apartment to regularly wear his sleeping mask at least, but people who have never slept in really dark rooms for prolonged time may simply not have the experience points here.
(1) Then again, the house I lived in that had them was nearly 100% concrete as most houses in Germany were. American houses, not so much. Sure would be useful here in Florida come hurricane season though.
This could be a sign you're not getting much restful sleep and that you may need those 10 - 12 hours to pay back sleep debt.
Right now I'm taking Gabapentin, which helps a little. So far the sleep specialists I'm working with (both a neurologist and a psychiatrist) haven't been able to find anything that helps more.