I was thinking of this too, oddly, also examples around books.
I vaguely feel like “no book” could also be parsed as… not one book, maybe? Like we’re saying there isn’t even one book on the subject. Maybe?
I dunno. The scenario that popped into my head was: what if you had a bookshop, where the shopkeeper would sometimes pick out books for you. If they said “I have no books for you today,” I’d imagine that they just generally didn’t find any books for you. Meanwhile if they said “I have no book for you today,” I guess I’d expect that you are waiting for a particular book, and it didn’t come in today. Somehow, there is a difference between the absence of a book and the absence of any books, even though in fact there are zero books in either case.
no book -> not a book
Yes, I think (2) is sort of like saying "not even 1" and more likely a response to someone saying there is a book, whereas (1) is a more common phrasing and is just saying how many books there are.