Greyed out button

When there's no history or website data to clear, the setting turns gray , for more info ☞ Clear the history and cookies from Safari on your iPhone, iPad, or iPod touch - Apple Support

A question -> do you have a MDM profile?

See this Apple article: Checklist: If you want to see if anyone else has access to your device or accounts

Checklist: If you want to see if anyone else has access to your device or accounts - Apple Support

See point 5.

Are you using Screen Time, check.-> go to Settings -> tap Screen Time -> scroll down -> turn it Off.

Then turn it On again.

Check if Celar History & Wbsite Data option is enable now.

Do you use Screen Time or not?

Can you give an answer?

Ant try this -> Go to Settings -> Safari -> scroll down to & tap Advanced -> tap Website Data -> dDlete all website dat.a

Thanks for your feedback & you're welcome.