Apple Books is not enabled on the Apple TV, and iTunes was stripped of audio books when the Apple Books (iBooks) app was pushed out in 2011. I am not sure why you are not using Audible it saves me a lot of money and plays from its app everywhere. The breaking news is most of the audible books you load on Apple Books comes from Audible anyway. I presently have 888 books in my Audible library, over 300 in my Kindle library. I don't use Apple Books except to load advance copies of books from Patreon. Did you know that Alexa can read Kindle books, It does a very good job considering the source. I loaded the Kindle book app in 2011, and Audible in 2014. There are so many freebee's on both Kindle and Audible they more than make up for the monthly subscription cost. $14.99 a month for Audible, Kindle Unlimited is $11.99 a month. Both are a bargain.
Tried to get my HomePod 2 too read a book from Apple Books on its own and it was a absolute no go.