What is real and what is fiction.  Some of us are interested in how the past connects to the present.  Others are interested in Rowoon's chiseled jaw line - this discussion topic isn't for them.  

The story apparently begins during the reign of King Hyo Jong 17 – a real historical person. He was the 17th King of the Joseon Era and his reign was from 1649 to 1659.

The King Hyojong Era (1649 – 1659)

King Hyojong of Joseon was the seventeenth king of the Joseon Dynasty of Korea from 1649 to 1659.  

Queen Inseon was the wife of King Hyo Jong, and the queen consort of Joseon from 1659 until her husband’s death in 1659.  She was a member of the Deoksu Jang clan,

Shaman Aeng-cho (a fictional/not historical person) was a female shaman during that era.  She was secretive.  She wrote the book “Spells of the Heavens”. She died by dismemberment

Jang Mu-jin (a fictional/not historical person) passed the military service exam and served “the King” (presumably King Hyojong). His name appeared multiple times in Joseon Dynasty Records which presumably means he did not die young.   He killed Shaman Aeng-cho.   Jang Shin-yu is a descendant of Jang Mu-jin.

Lady(?) Yoon (a fictional character) communicated with Aeng-cho, according to the web site viewed by Shin-yu (my poor translation)

Assuming the writers are following real history (the reign of King Hyo Jung) and placing fictional characters within the era, I believe that Aeng-cho and Jang Mu-Ji are fictional characters and have no relationship to the actual palace intrigue of the time. 

The MDL commenter Shy  translated the page that Hong-jo read from the internet.  It contains a much longer description of the relationship between Shaman Aeng-cho and Lady (?) Yoon.  Here is the link to her post:  Destined with You (2023) - MyDramaList 

For those who haven't made the connection (and it was poster Shy connected the dots), YOON is the surname/last name of the SFL - Yoon Na Yeon.