[2022] The character search settings and game rules are not saved

That does sound exactly as if your antivirus is preventing the game from writing out changes to those files. Which one do you use? You are such ck3.exe is in all its exceptions lists?  

That's the Ransomware-Apps Allowed Through list, is that right?

What if you make a new Windows user, log in as that, and try the game there? Any different?  

Well, that shows that either there is a problem with your original user profile, OR there is indeed something on your machine interfering with write access to the Documents/Paradox Interactive/CK3 folders - but only for that one user. How very odd!