Good morning xmanstc!
I see that you've turned on unrestricted access for web content using parental controls on the iPhone, but you're still unable to use Private Browsing. I'll be happy to help out.
Have you tried restarting yet? If not, try that now: Restart your iPhone, iPad, or iPod touch. Then see if the Private tab is working again. If that doesn't help, try turning off restrictions completely to see if that brings the option back. You can do this by going to Settings > Screen Time > Content & Privacy Restrictions > Content Restrictions. Turn off Content Restrictions completely. If this brings back the Private Browsing option back, then go back to the Settings and readjust the content restrictions again as needed: Use Screen Time to get insights about how you use your device.
Keep us updated!