The Tailwind CSS Intellisense extension struggles with providing auto-competion and css intellisense when used inside the classed method. However, Tailwind CSS has a solution for this.

Setting Experimental Class Regex

By adding this script to your settings.json in the workspace or globally, you can set the regex for the classed method to match the class names and provide intellisense.

{
  // ... settings
  "tailwindCSS.experimental.classRegex": [
    ["classed(?:\\.\\w*)?\\(([^)]*)\\)", "[\"'`]([^\"'`]*).*?[\"'`]"]
  ]
}

Tailwind CSS Intellisense will now match the class names and provide intellisense for the classed method.