Ah, the key concepts like "state" and "government", or even "public order" in medieval Europe and how they actually worked are often not so straightforward to define as generally assumed in popular culture, and many relevant literature probably belong to at least 'intermediate' or more advanced milieu (that's at least why they had largely been omitted in the current booklist).

If you are really, really interested in this topic, I'd recommend these books as departure points, though beware that some of them might not be so readable as those in the subreddit's booklist.

(General/ including Histriographical or Conceptual)

• Althoff, Gerd. Family, Friends and Followers: Political and Social Bonds in Early Medieval Europe, trans. Chrostopher Caroll. Cambridge: Cambridge UP, 2004: It is not only the institution and the law, but social ties like "friendship" between the lord and followers that really mattered in earlier Middle Ages, in the world (almost) without the concrete concept of statehood. Translated from German original (1990).
• Clanchy, Michael. From Memory to Written Record: England 1066-1307. 3rd rev. ed. Oxford: Wiley Blackwell, 2010: also found in the subreddit's book list. This book, focusing on the changing mentalities / increasing reliance on the documents in course of post-conquest England should be must-read also for the topic.
• Fletcher, Christopher, Jean-Philippe Genet & John Watts. Government and Political Life in England and France, c.1300–c.1500. Cambridge: Cambridge UP, 2015: I suppose this collection of essays is the closest one OP is originally looking for.
• Strayer, Joseph. On the Medieval Origins of the Modern State. Princeton, NJ: Princeton UP, 1970.
• Wickham, Chris. Medieval Europe. New Haven: Yale UP, 2016, Chaps. 6 (pp. 99-120) & 8 (pp. 141-169): The standard overview of the Middle Ages also includes sections with passing mentions to the rise of government in the High Middle Ages.

(England - mainly Norman and Angevin Period)

• Bartlett, Robert. England Under the Norman and Angevin Kings, 1075-1225. Oxford: OUP, 2000.
• Crouch, David. Medieval Britain, c. 1000-1500. Cambridge: Cambridge UP, 2015, Chap. 5 (pp. 103-36).
• Huscroft, Richard. Ruling England, 1042-1217. Harlow: Pearson Longman, 2005; 2nd ed. London: Routledge, 2016.

(France)

• Baldwin, John W. The Government of Philip Augustus: Foundations of French Royal Power in the Middle Ages. Berkeley: U of California Pr., 1986.
• Jordan, William C. Louis IX and the Challenge of the Crusade: A Study in Rulership. Princeton, NJ: Princeton UP, 1979.

(Germany)

• Wilson, Peter H. The Holy Roman Empire: A Thousand Years of Europe's History. Harmondsworth: Penguin, 2016: I'd avoid to recommend the book of nearly 1,000 pages, but this is one of the few Anglophone books also alluding to the territorial states.....

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BTW, the subreddit's AMA on CK3 and CK2 might includes some posts relevant to these books as well as OP's question:

• Crusader Kings III/Medieval Period Flair Panel AMA: Come Ask Your Questions on Incest, Heresies and Video Game History!
• Media Monday: Crusader Kings II