Is Tailwind class binding possible through Storyblok?

You need to add Complete Class Names.
As there is no w-1/2 in your code, TW won't generate the class.

You can workaround the issue by adding the class to safelist.
Doc: https://tailwindcss.com/docs/content-configuration#safelisting-classes

module.exports = {
  safelist: ['w-1/2'],
  //...
}

Then w-1/2 utility will be generated regardless if it shows up in your code or not.

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