Is it normal to stay up late the next day without being sleepy?

Normal. I feel this way sometimes. I went to bed late, but I wasn't so sleepy the next day. This situation is usually that a busy day takes up energy and the brain is more active. It is said that Edison used to take only a few naps a day when he was busy, but he became the king of inventions throughout the ages. But of course, this is not worth advocating. Try to sleep a little more every day. Staying up late for a long time is not good for all functions of the body. Take good care of yourself!