@Federico Coppola, Thanks for posting in Q&A.
On my ADE enrolled device, I find the "Clear History and Website Data" is not greyed out after I browse some websites. From your description, I notice yours are greyed out. After researching, I find there are some settings can block the function to use:
https://appletoolbox.com/cant-delete-safari-history-on-iphone-ipad-fix/
Note: non-Microsoft link, just for the reference.
Given the situation, please check if any device restriction is applied to this device and if any related setting is set there: If yes, remove the policy and see if it works
https://video2.skills-academy.com/en-us/mem/intune/configuration/device-restrictions-ios
Hope it can help.
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