That sounds right, sleep is just the beginning of recovery from burnout. I can get pretty productive for some deadlines, working nonstop, but if there is too much to do, it can become painful to work or think, and the productivity can even come to a complete halt. Only after a week or more can I do anything. So, lessons learned a few years ago, it's best to keep overworking to short bursts, and there are no miracles.
That theory would only work if sleep caused me to feel refreshed. But I don't think any of us have ever had the experience that more sleep lead to more awakeness. It's not as if we are well rested after 8 hours of sleep, and even more energized by 9 hours of sleep, and even more energized by 10 hours of sleep, and even more energized by 11 hours of sleep, etc.
I think most of us have had the experience of over-sleeping, and then being strangely groggy all day. Certainly, most of my friends have had that experience.
That may be because your sleep deficit is say 20 hours and your need 8 (6 if lucky) to break even so you need something like 10 hours a day for 10 days to catch up.
All this is to say I occasionally feel groggy but if I consistently sleep “a lot” I feel great after a few days.