Why would "I have the final books" not also be correct?
Feel free to report.
Is "I have the latest books" also correct?
According to http://www.mijnwoordenboek.nl/vertaal/NL/DE/laatste I'd guess yes.
last and latest have a different meaning in English. last is general while latest means the most recent
Can boek also be booking an appointment or something?
What is the singular form of laatste?
Adjective declension depends on more than just a singular or plural noun, for more info: https://www.duolingo.com/comment/3888221
Ik heb het laatste boek
Singular is equal in this case as boek is a "het"-word (neuter)
Laatste means the last edition books - new?