Hypnagogia, awesome... I have something I can look up. It is indeed what I experience sometimes.

From the article on wiki, two sections jumped out at me:

Subjective interpretation

Hypnagogic phenomena may be interpreted as visions, prophecies, premonitions, apparitions and inspiration (artistic or divine), depending on the experiencers' beliefs and those of their culture.


and


Insight

This process can even lead to genuine insight into a problem, a well known example being the story of August Kekulé's discovery of the structure of benzene.[40] Many other artists, writers, scientists and inventors—including Beethoven, Richard Wagner, Walter Scott, Thomas Edison and Isaac Newton—have credited hypnagogia and related states with enhancing their creativity.[41] Also, Samuel Taylor Coleridge's famous poem Kubla Khan was (according to its author) "a fragment" inspired by an opium-induced dream, its composition interrupted by a person from Porlock after which Coleridge found he had forgotten all but some "eight or ten scattered lines and images".[42]

It's good to know that I'm far from the only one who experiences this.