drowse
To be half-asleep, gently drifting toward sleep but awake.
To drowse means to be in that peaceful, half-asleep state where you're not quite awake but not fully asleep either. When you're drowsing on the couch on a lazy Sunday afternoon, your eyes might flutter closed, your thoughts drift and wander, and you feel wonderfully relaxed and cozy.
You might drowse during a long car ride, lulled by the gentle motion and the hum of the engine. Students sometimes find themselves drowsing in a warm classroom after lunch, fighting to keep their eyes open. A cat drowsing in a sunny window looks utterly content, occasionally twitching an ear but mostly just soaking up the warmth.
Drowsing is gentler and more pleasant than simply feeling sleepy or exhausted. It's that delicious, drowsy feeling when your body is completely relaxed and your mind floats between waking and sleeping. Unlike actually falling asleep, when you're drowsing, you're still somewhat aware of your surroundings but too comfortable to pay much attention to them. The word captures that specific, hazy contentment of drifting toward sleep without quite getting there.