Right at this exact moment if all your friends & family & law enforcement saw all your search engine history, would you be embarrassed? Anything you'd want to delete before they see it?
And I learned by watching the news in cases like Jared fogle, nothing can actually ever be deleted from hard drives & clouds. Even everything we've ever posted to Reddit and thought we deleted it, everything is always available somewhere for the experts to find.
Stuff can absolutly be deleted. If you overwrite the stuff that was previously saved there it's gone. The point is that cloud providers often just don't delete your stuff. And whatever you do your network provider allways knows what you search for.
Oh most social media probably keeps a copy. But your search history is usually stored locally, so it's possible to delete that. Your internet provider only has a history of all sites that where visited via your internet connection and is unable to backtrack something to a specific device.