Being the earliest chronological entry in the series taking place something after The Wonderful Wizard of Oz would have ended, the Scarecrow being the King of Oz is with the Tin Man and Lion as suddenly gun shots ring out as General Jinjur and her soldiers invade the palace.
Also, the Tin Man and Scarecrow escape on Lion which is different than them along with Tip and Jack Pumpkinhead escaping the invasion by use of the flying Gump.
It is presumed that Glinda took Ozma out of Gillikin Country out of the custody of Mombi but this has yet to be mentioned in detail.
Before her death, Hibiscus Lemon mentions Ozma, but she could have been referring to a previous Ozma in a concept similar to that which is mentioned in the Oz books and the Wicked series.
The titles and descriptions of in-universe books are mentioned as:
53 volumes of The Collected History of Oz: Its Landscapes, Customs, and Peoples (Scarecrow was only on Volume 23)
Anthropmorphicum Catalogarium: A Bestiary of Magical Creatures, Their Diets & Their Habitats
Tax Codes of the Quadlings
How to Cook for a Rigmarole
Despots of Oz: Their Way, or the Highway! which he uses to look up General Jinjur who had been planning her invasion for a long time but paused after hearing Dorothy companions had been given "mighty gifts of magic". Interestingly enough, other entries include articles about: Dr. Pipt, Eureka (she had orginally came to Oz inDorothy and the Wizard in Oz), Evoldo (he had been dead before the events of Ozma of Oz), Gayelette, and the Hungry Tiger.