You can use the Property Manager window in Visual Studio for managing common properties of C++ projects, but there appears to be no equivalent to this for C# projects.
Is there a way to set common settings across multiple projects? Examples of things I'd like to do:
A plugin, macro, or extension would all be acceptable.
There is no a real equivalent of Property Manager for C# projects. However, if the goal is to share common settings across multiple projects, you can create a NuGet package with .props file defining the shared properties and reference it in your C# projects - VS will automatically import it at build time.
.props and .targets inclusion is supported as of NuGet 2.x. Tip: make sure the .props file name matches the NuGet package id, otherwise it won't be included. You can see an example here.