Linking the Steam account doesn't give you Factorio on Steam, it only allows you to download the game from factorio.com and use the mod portal / multiplayer server if you originally bought the game on Steam.

To get the game on Steam (originally bought on factorio.com) you'll need to get a Steam ...

I've gone through factorio.com, scrolled to the bottom of the account page, linked my steam account, but when I close and reopen steam factorio isn't in my library.
I do have family linking with my brothers steam account and he already had factorio in his library, but I'm not sure if that's what ...