Yes, I'm obviously trying.
My first attempt was a tiny change in the KCookieServer/KCookieJar API to
let people search just for persistent cookies.
But it failed.
I'm currently working on a second attempt following the same approach. If
not, I though about implementing a different jar for the private sessions.
But this second idea is probably an "hard" change in the kde cookie jar.
I fear that "private sessions" are exactly the opposite idea around what
the "monolithic" & "share it with every app" kde cookie jar is builded.