Drowsy means heavy-eyed and half asleep — the state just before sleep, or the one a warm room and a large lunch produce. It is milder than exhausted and less deliberate than sleepy.
The word appears constantly on medicine packaging, and that is where most learners will meet it: this medicine may cause drowsiness, do not drive or operate machinery. That fixed warning is worth learning whole. The noun is drowsiness, and the verb form drowse exists but is rare and literary. Compare sleepy, which is the ordinary word, and lethargic, which is about energy rather than sleep.
1adjectivedrowsyHalf asleep and hard to keep awake.
“The tablets made her drowsy for most of the afternoon.”
synonyms: sleepy, dozy, somnolent
2adjectiveplaceOf a place or a time, making people feel sleepy.
“It was a drowsy afternoon and nothing got done.”
drowsy is a state of near sleep.
Also accepted in games: sleepy
From drowse + -y, despite the fact that drowsy (1520) is recorded before drowse (1570). Compare Old English drūsian (“to droop, drowse, become languid”).
Etymology from Wiktionary, CC BY-SA
Practised in Body & Health, Sharper Adjectives