Can you turn browsing mode on for me?

Enable Private Browsing

Settings > Screen Time > Content & Privacy Restrictions > Content Restrictions > Web Content > Unrestricted Access [Tick]

Disable Private Browsing

Settings > Screen Time > Content & Privacy Restrictions > Content Restrictions > Web Content > Limit Adult Websites [Tick]

Did you review the steps provided in the support article you arrived here from on how to enable Private Browsing in the Safari app on your iPhone?