Error: PostCSS plugin tailwindcss requires PostCSS 8

You're integrating Tailwind with a tool that relies on an older version of PostCSS. You can use this doc https://tailwindcss.com/docs/installation#post-css-7-compatibility-build

npm uninstall tailwindcss postcss autoprefixer

then

vue add tailwind 

to use the vue cli plugin https://www.npmjs.com/package/vue-cli-plugin-tailwind