There is a noun meaning 'book of fiction': 'novel'. But there doesn't seem to be a noun meaning 'book of poetry/poems'. Or is there?
Lexico gives the word
1 A published collection of poems or other pieces of writing.
an anthology of European poetry
It is usually used for poetry, for example:
There isn't such a word. There is a noun phrase "slim volume" that has the chief meaning of "a small book of poems", but this is now a little derogatory:
1920 E. Wallace "The Daffodil Mysteries" - Thornton Lyne was a store-keeper, a Bachelor of Arts,..and the author of a slim volume.
1979 Church Times "Friends will..welcome a slim volume of his poems that has come out."
A novel is not a book - it is a particular type of story.
OED: Novel (n.) A long fictional prose narrative, usually filling one or more volumes and typically representing character and action with some degree of realism and complexity; a book containing such a narrative.
So "He published his novel" approximately means "He published his story." Thus, not all story books contain novels.
The OED regards poetry-book as something that can be hyphenated, or even written as a single word.
n. 1772 T. Bridges Burlesque Transl. Homer (rev. ed.) Ded. p. ii Your book's a poetry book, is not it?
1847 W. M.> Thackeray Vanity Fair (1848) xii. 103 She wrote whole pages out of poetry-books without the least pity.
2000 San Diego Union-Trib. (Nexis) 18 Apr. (Computer Link Section) 18 Bruce Lansky's books are among America's best-selling children's poetrybooks.
However I do understand your sense that there should be a specific word - of course if one is speaking of psalms one has psalter.