Vulkan: Provide a more accurate method of detecting drivers/vendors

This is needed to differentiate between the open-source Mesa drivers and
their binary counterparts for Intel and AMD.

Source/Core/VideoBackends/Vulkan/VulkanContext.h

@@ -114,6 +114,7 @@ private:
   bool SelectDeviceExtensions(ExtensionList* extension_list, bool enable_surface);
   bool SelectDeviceFeatures();
   bool CreateDevice(VkSurfaceKHR surface, bool enable_validation_layer);
+  void InitDriverDetails();
 
   VkInstance m_instance = VK_NULL_HANDLE;
   VkPhysicalDevice m_physical_device = VK_NULL_HANDLE;