Can someone brief explain to me why I can't use NuGet packages on my Shared Project?
Take a look at the guide on Shared Projects for more background on what they are and how they work: https://developer.xamarin.com/guides/cross-platform/application_fundamentals/shared_projects/
Shared Projects are basically just a folder with your code files. They don't build any output like other project types you are used to. Whatever is in them gets linked into the projects that reference it. In this case, you would instead add the NuGets to your iOS/Android/Windows projects. Then, you will have access to them in the Shared Project code.
Hope that helps!
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