1. Make sure you have these npm dependencies installed

• Hugo v0.92.0 (May work with older versions too, but not tested)
• tailwindcss
• postcss
• postcss-cli
• autoprefixer

2. Run npx tailwindcss init -p to create a TailwindCSS and a PostCSS config file.
3. Add this to your tailwind.config.js file:

   {
        content: ['./layouts/**/*.html', './content/**/*.md']
   }

4. Run hugo or hugo server -D --watch to see the result

Read the full article here: https://dev.to/jonas_duri/how-to-use-tailwindcss-30-without-external-npm-scripts-just-hugo-pipes-2lg9
This already includes the proposed changes from @nnooney: gohugoio/hugo#8343 (comment)