What is the Public Domain, and How Does This Affect "A Nightmare in Oz?"
The term “public domain” refers to creative materials that are not protected by intellectual property laws such as copyright, trademark, or patent laws. The public owns these works, not an individual author or artist. Anyone can use a public domain work without obtaining permission, but no one can ever own it.
What this means, ultimately, is that Baum's world is open to use in any subsequent storytelling offered by newer writers, including myself. "A Nightmare in Oz" contains a handful of those characters and involves them in a new story arc that exists 100 years after the events of the earlier books, set in a time frame that is equivalent to the current year of Earth.
Copyright laws have permitted the possibility of renewals for previously-held intellectual properties, but now those extensions are starting to expire further, allowing for access to later volumes in the Famous Forty. According to Stanford:
As of 2019, copyright has expired for all works published in the United States before 1924. In other words, if the work was published in the U.S. before January 1, 1924, you are free to use it in the U.S. without permission. These rules and dates apply regardless of whether the work was created by an individual author, a group of authors, or an employee (a work made for hire).
Because of legislation passed in 1998, no new works fell into the public domain between 1998 and 2018 due to expiration. In 2019, works published in 1923 expired. In 2020, works published in 1924 will expire, and so on.
In light of this development, many aspiring writers seeking a slice of the Oz mythos have access to use characters created in the following books in the original canon:
The Baum Books:
The Wonderful Wizard of Oz 
The Marvelous Land of Oz 
Ozma of Oz 
Dorothy and the Wizard in Oz 
The Road to Oz 
The Emerald City of Oz 
The Patchwork Girl of Oz 
Tik-Tok of Oz 
The Scarecrow of Oz 
Rinkitink in Oz 
The Lost Princess of Oz 
The Tin Woodman of Oz 
The Magic of Oz 
Glinda of Oz 
The Plumly Thompson Books
The Royal Book of Oz 
Kabumpo in Oz 
The Cowardly Lion of Oz 
In addition, several later titles in the latter part of the series never had their initial copyright renewed:
By Plumly Thompson:
The Wishing Horse of Oz [1935; in public domain since 1963]
Captain Salt in Oz [1936; in public domain since 1964]
Handy Mandy in Oz [1937; in public domain since 1965]
The Silver Princess of Oz [1938; in public domain since 1966]
Ozoplaning with the Wizard of Oz [1939; in public domain since 1967]
By Jack Snow:
The Magical Mimics of Oz [1946; in public domain since 1974]
The Shaggy Man of Oz [1949; in public domain since 1977]
Subsequently, a new Oz book under the 19-long stretch of Thompson books will come into public domain each year for the next 11 years, beginning with Grampa in Oz later this year  and ending with Speedy in Oz in 2030.
Once a book comes under public domain, it also means that they can be distributed freely, via on the internet or in new additions provided by book retailers. Each of these is available in digital text on several public web sites, including the Fan Wikipedia dedicated to the series (direct link to those texts here). Occasionally, Barnes and Noble will publish exclusive leather-bound editions of a variety of old novels, including the Oz books; this is because they no longer have to purchase the rights to the stories, as each of them have fallen out of copyright rule. With the impending release of many of Plumly Thompson's contributions, it will also become possible to see her novels line those shelves in the near future (some of her texts have been out of print for some time).
What you will read in "A Nightmare in Oz" involves many of Baum's original characters, all of whom are verified as part of the public domain.
For more information on copyright laws in the United States, visit the Stanford University page here.