Without knowing for certain, I’ll say that it works like regular Safari, so anything regular Safari would store to disk gets stored to a /tmp directory attached to the individual session and cleared on session end.
I believe it'd stay there for a day, a week, a month something like that, but eventually would get cleaned. A reboot should do it too. - Not tested any of this, but basing it off of how a /tmp folder usually works. - What I have tested though is actually that if a page in private mode is open when your device runs out of power the same page will open next you get juice and open Safari - though that was a few iOS updates ago.