Do Safari private tabs stay open after iPhone shutdown?
I just checked this on my iPhone 6 running iOS 10.3.3. I opened a private browsing tab and went to a site then powered my iPhone off. 

When it restarted I opened Safari again. My private browsing tab opened up to the exact site I was on when I powered off. 

So I think you're busted on this one. But you've learned a valuable lesson about private browsing and always having a passcode on your device :-).