Warzone
Warzone
You don't need to reinstall MW after installing Warzone and the MW campaign with multiplayer enabled.
It seems you likely won’t need anything extra. Your first installation file was probably about 150GB, and you got it together with the other package.
You'd likely need to add MW separately even after installing Warzone, because much of the content is already present. This would probably result in a much smaller download size.
I recently purchased Modern Warfare and needed to save the full game. I had already downloaded Warzone, but the complete version was still required (about 89 gigabytes).