OK, I did a little experimenting this morning, and it seems that the " ^partitionkey=%28http%2...." versions of cookies do not function to save logins or website preferences.
I used the Amazon.com website for a trial.
I cleared out my Amazon cookies, visited the website, signed in, and set my preference for saving my browsing history. I then opened CCleaner, and I see four cookies:
After a few trials of having CCleaner save each of the individual cookies, one at a time, then cleaning the others, I found that having CCleaner save only the www.amazon.com^partitionkey+%