And those things all have their own words for their authors, as well.
poetry - sha3r
poet - shaa3r
composition (the noun of the verb) - ta2leef
composition (the thing written) - mu2allaf
composer - mu2allef
letter, correspondance - resala
messenger - rasool
correspondent (like a news reporter) - murasel
You can also use kaateb for the author of a letter or perhaps a poem, but not really a symphony. Just like you wouldn't use author. Pardon the use of the numbers in words - it's how people represent letters that aren't in English in Arabic.
Note, by the way, that your examples showcase the same pattern in English - the author of "poetry" is a "poet", the author of a "composition" is a "composer" etc.
I was more replying to your comment than continuing GP's argument, but I believe what they were trying to say is that the system used in Arabic is very regular and predictable. If I didn't know English, I might say that the person who writes poems is a poemer. Or a poetrier. I might try to use "to poetry" as a verb.
I wouldn't really make that argument because through learning Esperanto I realized that a truly logical language would make nearly no sense. You can't just invent any word you like in Esperanto, although it is sometimes billed that way, and you can't in Arabic. But at least it's very predictable and, at least, you can derive the meanings of an already-written text fairly easily.
The problem (touched upon in the OP) is that each dialect has its own domain of vocabulary, so even apart from foreign/native language influences, the classical vocabulary that sticks around in each dialect varies widely from one place to another. Some people use the verb for "work" to mean "work" and some use the verb for "preoccupy oneself" to mean "work."
2 of may favorite things about the language: 1/ fun fact is that the vast majority of verbs have only 3 letters in them 2/ Pronouns make a distinction between one, two or more people, and even indicate whether the subject is present or absent. I find it extremely powerful.
I don't see why the word for "author" has to be derived from the same root as "book", logically speaking. There are a great deal more things than books that have authors.
The reason why this particular root that you've picked produces differences between "book" and "library" in most European languages is because they had two major sources from which their roots were borrowed: Latin (where "book" is "liber") and Greek (where "book" is "biblio"); and both roots were borrowed and used in this case. However, for most roots, the principle is exactly the same in European languages - a single common root produces a whole family of words, and new words are derived as needed. It's not something that's unique to Arabic.