Alrighty, I have figured this out. It turns out that Windows VST plugins need to be built with a statically linked runtime library, as described in this thread: Do plugins need Visual Studio redistributable?
By default Projucer uses Visual Studio’s default Runtime Library setting, which I believe is “Use DLL runtime”. In VS it is called /MD or “Multi-Threaded DLL”. I gather that the /MD setting requires the end-user to have the Visual C++ Runtime Redistributable installed, otherwise the VST will break.
In my case the VST was broken until the first reboot after I installed Visual Studio. The Windows Update thing was a red herring.
Explicitly setting Runtime Library to “Use Static Runtime” in Projucer fixed the problem.