I've tried to replicate your code using SDL preview-3.1.6 and both the extension number and the required extensions get reported correctly. The steps I followed are:

• git clone https://github.com/libsdl-org/SDL.git SDL
• Open and build SDL/VisualC/SDL.sln
• Create a new project with your code
• Add an include directory that points to SDL/include.
• Add a linker path to SDL/VisualC/x64/Debug
• Copy SDL/VisualC/x64/Debug/SDL3.dll into the same folder as the exe.

If after following these steps you get the same error you need to check that you have a good Vulkan installation and that you are linking correctly with SDL.

First thing I would try is to check that the demos in the Vulkan SDK work. You can find them at %VULKAN_SDK%/Demos.

After that I would test a basic triangle sample you can find online. For example:

• git clone --recursive https://github.com/SaschaWillems/Vulkan.git
• cmake -G "Visual Studio 16 2019" -A x64
• Then set the Triangle demo as the default project, then build and run it

If the Vulkan Demos or the Triangle Example work it means you have a problem with SDL. Check that you are linking with the correct lib/dll or try with SDL2.