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They can do it at the border or within 100 miles of it
Pretty sure that’s just a US thing (including declaring that international airports are “borders”). Other countries will have other laws.
Still best to bring a burner instead of your real device if you’re passing through international customs, though, even if both countries involved claim to be respectable Western democracies. Just in case.
Pretty much any country can search you at their borders if you’re seeking to cross in, yes (there may be some special cases—I’m not sure that an EU citizen crossing from one EU country to another is normally subject to search), but most countries only do that at border checkpoints, or if you’re caught crossing illegally. “More than an hour’s drive away from the border is still the border” is not the law in most places, as far as I know.