The audio inflection on можешь indicated a question which confused me and I translated as "can you" instead of "you may." I see now the sentence does not have a question mark, but the audio is confusing.
Yes, you are right. The intonation sounds more like a question to me (a native speaker).
Why is взять instead of брать, when the books were not already taken (and may never will)?
Ты можешь взять эти книги = You can (may) take (all of or part of) these books (right now or later).
Ты можешь брать эти книги = you can take (1 or more of) these books from time to time and return them (like in the library).
so брать only works in the borrowing sense?
Only if you are going to do it repeatedly.
The perfective is confusing for UK English speakers.
Perfective is used for one-off actions that have been or will be completed, depending on the tense used.