Yes, in the Han Dynasty, the position of Secretary of State was held by eunuchs. During the reign of Emperor Wu of the Han Dynasty, the position of Zhongshu Ling was held by eunuchs. They were responsible for organizing the palace library files in the emperor's study and had frequent contact with the emperor. In the Western Han Dynasty, the Zhongshu Ling belonged to the eunuch organization of the inner court.

The Star Fox team could be main characters. Fox McCloud might interact with the Secretary of State, perhaps providing military advice or being involved in diplomatic missions that require their combat skills.
Regarding Han Liming's family background, I didn't find any official reports, so I can't give an accurate answer. You can ask me some other questions and I will try my best to help you. While waiting for the TV series, you can also click on the link below to read the classic original work of " A Record of a Mortal's Journey to Immortality "!
In Joy of Life, Si Lili's true identity was a descendant of the Qing royal family. She was the granddaughter of the Qing prince. During the coup, her grandfather and father were killed one after another. She and her mother fled to Northern Qi and were taken in by the Northern Qi Empress Dowager. For revenge, she changed her name to Si Lili and became a spy Northern Qi had planted in the Qing Kingdom. Thus, Si Lili was a descendant of the Qing royal family and a spy for Northern Qi.
Si Lili was a character in the novel " Joy of Life " and its derivative works. She was the top actress of the Drunken Immortal Residence in Jingdou, Qing Kingdom. On the surface, she was the top actress of the Drunken Immortal Residence in Jingdou, but in reality, she was a spy of Northern Qi lurking in the Qing Kingdom.
In Joy of Life, Si Lili's real identity was a spy sent by Northern Qi to the Qing Kingdom and a Northern Qi noble consort. She used her status as Courtesan Belle to spy on Qing Kingdom's intelligence and played the role of raising Zhan Doudou and Fan Xian's daughter, Red Bean Rice.
In Joy of Life, Si Lili's real identity was a spy sent by Northern Qi to the Qing Kingdom and a Northern Qi noble consort. She used her status as Courtesan Belle to spy on Qing Kingdom's intelligence and played the role of raising Zhan Doudou and Fan Xian's daughter, Red Bean Rice. In the end, she married the Northern Qi Emperor, Zhan Doudou, and became the Imperial Noble Consort of Northern Qi.
I recommend " The Eunuch's Imperial Study " to you. This is a eunuch novel that traveled through the Qing Dynasty. The protagonist traveled to the Qing Dynasty and became a eunuch. In order to survive, he had to hide in the royal study. The plot of the novel was very compact and exciting. The protagonist experienced many unimaginable things under the identity of a eunuch.
The following are some recommended novels about Qing Dynasty eunuchs: The Eunuch's Imperial Study, Fake Eunuch: I'm the Crown Prince of the Former Dynasty, The Daughter of a Crazy Concubine in a Prosperous Age, Fake Eunuch: From Salted Fish to Overlord of the World, Three Lives Crossing the Tribulation Fate, Top Eunuch, and so on. These novels covered different plots and styles to meet the needs of readers.
In the Ming Dynasty, eunuchs first had to go through layers of selection and interviews. After being selected, they would be castrated in the official castration field before they could enter the palace to become eunuchs. There were many levels of eunuchs. When they first entered the palace, they could only serve as the chief clerk, the chief attendant, and the imperial guard. If they performed well, they could be promoted to the supervisor, and then to the junior supervisor. The superior of the junior supervisor was the eunuch. The eunuch was the highest commander of the 24 yamens (12 prisons, 4 departments, and 8 departments) of the Ming Dynasty. In the Ming court, eunuchs had many lives and roles. Some eunuchs were not completely chaste and might be connected to the concubines. There were also eunuchs and palace maids who developed a "eating relationship" to take care of each other. They were responsible for all kinds of affairs in the palace. The eunuchs of different yamens were responsible for different jobs. For example, the ceremonial supervisor was in charge of internal and external memorials, similar to the emperor's private secretary. The imperial horse supervisor was in charge of the imperial military seal and military power. The palace supervisor and the governor were in charge of cleaning and hygiene. Eunuchs were also the emperor's chess pieces against the civil officials and played a pivotal role in the politics of the Ming Dynasty. For example, a eunuch like Wang Zhen could lead an army to war, but his improper command also led to serious consequences. In addition, there were also web novels with the theme of "mingling in the Ming Dynasty as a eunuch", describing the plot of mingling in the last golden age of the Ming Dynasty as a lively club boss.
Well, it could be about the Secretary of State in Corneria dealing with political intrigue. Maybe they are involved in negotiations with other planets or factions in the Star Fox universe.