[Vuejs]-How to get CSS IntelliSense to work on a Nuxt project?

This is the normal behaviour:
https://github.com/Microsoft/vscode/issues/27635

Try the plugin:

IntelliSense for CSS class names in HTML
  or
HTML CSS Support

Source: https://code.visualstudio.com/docs/languages/css

And of course Vetur a must-have plugin for vue development in vscode.