Intellisense for available 'using/import's in C# with Visual Studio Code

I just went ahead and made the extension:
https://marketplace.visualstudio.com/items?itemName=Fudge.auto-using#overview
Currently it supports only the base C# libraries but I can make it use additional nugget libraries as well if there is demand for that. As of 24/11/2020 the official C# extension supports this feature, see other answer.

If you use "C# extension" for VSCode (this https://marketplace.visualstudio.com/items?itemName=ms-dotnettools.csharp)

you can try follow next steps:

1. Right click on C# extension
2. "Extension settings"
3. In opened "Settings" tab, add import in search area
4. Enable Checkbox (Screenshot of this step)
5. Enjoy autoimport without "special" extension (Screenshot)