Not specifically about kings but — I recommend The Time Traveler's Guide to Medieval England by Ian Mortimer, for a very thorough look at daily life in this era.

More specifically about kings, ACoUP has a great writeup [0] on royal legitimacy and the various purposes of the king's court in the context of my favorite medieval shenanigans simulator, Crusader Kings III.

[0] https://acoup.blog/2022/02/18/miscellanea-thoughts-on-ckiii-...