i cant delete my search history

I had the same problem on deleting search history as well.

You have to go to….. settings>screen time>Content and Privacy Restrictions>TURN OFF CONTENT AND PRIVACY RESTRICTIONS

NOTE: If you have a parent who set up a pin you will need that for it to work

Hopefully this helps anyone who has experienced the same problem as me

Delete history, cache, and cookies

1. Go to Settings > Safari.
2. Tap Clear History and Website Data.

Clearing your history, cookies, and browsing data from Safari won't change your AutoFill information.

When there's no history or website data to clear, the button to clear it turns gray. The button might also be gray if you have web content restrictions set up under Content & Privacy Restrictions in Screen Time.

To visit sites without leaving a history, turn Private Browsing on.

See Clear the history, cache, and cookies from Safari on your iPhone, iPad, or iPod touch - Apple Support.