Your Steam account will know what games you have. Which is why you can go to your games library right-click a game and select delete local content. The game will be greyed out, buy you can download it at anytime again.
WOrks the same if you buy a new HDD/SSD. Just install steam, log in with your account details, when you look at your library you'll see all your games.
You just have to right-click and select install game. When it finishes you can play it.
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