What a security aware student!
As mentioned, the only way to properly keep track of web activity is with a forced install of a third-party web filter. You should never count on gaining access to the local built-in web history, as it always requires knowledge of the current password used on the device. You could even disable it for students, if you want, and don't get pushback from them.
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https://wheretofind.me/@NoSubstitute