Vulkan: Refactor initialization to only use a single instance

Hopefully will fix the crash in vkDestroyInstance on the NV Shield TV,
and likely reduce boot times slightly for drivers that take a while
to create instances.

Source/Core/VideoBackends/Vulkan/VideoBackend.h

@@ -10,6 +10,7 @@ namespace Vulkan
 {
 class VideoBackend : public VideoBackendBase
 {
+public:
   bool Initialize(void* window_handle) override;
   void Shutdown() override;