Is it possible to have TailwindCSS with VueJS3 without Vite? Error with PostCSS 8

I have almost the same problem as this question :

PostCSS 8 Error When Installing Tailwind CSS in Vue 3 (v3.2.10) without Vite (PostCSS 8 is supported)

I followed Flydev's answer and performed the same procedure :

vue create new-project
cd new-project
npm install -D @vue/compiler-sfc tailwindcss@latest postcss@latest autoprefixer@latest
npm run serve

Node and Vue/cli versions are perfect. I made the changes in my package.json folder, delete package-lock.json and then run npm install

My package.json :

{
  "name": "new-project",
  "version": "0.1.0",
  "private": true,
  "scripts": {
    "serve": "vue-cli-service serve",
    "build": "vue-cli-service build",
    "lint": "vue-cli-service lint"
  },
  "dependencies": {
    "core-js": "^3.6.5",
    "vue": "^3.2.11"
  },
  "devDependencies": {
    "@vue/cli-plugin-babel": "~4.5.0",
    "@vue/cli-plugin-eslint": "~4.5.0",
    "@vue/cli-service": "~4.5.13",
    "@vue/compiler-sfc": "^3.2.21",
    "autoprefixer": "^10.4.0",
    "babel-eslint": "^10.1.0",
    "eslint": "^6.7.2",
    "eslint-plugin-vue": "^7.0.0",
    "postcss": "^8.3.11",
    "tailwindcss": "^2.2.19"
  },
  "eslintConfig": {
    "root": true,
    "env": {
      "node": true
    },
    "extends": [
      "plugin:vue/vue3-essential",
      "eslint:recommended"
    ],
    "parserOptions": {
      "parser": "babel-eslint"
    },
    "rules": {}
  },
  "browserslist": [
    "> 1%",
    "last 2 versions",
    "not dead"
  ]
}

npm run serve works ! Great ! But not Tailwind :(

So I looked at the documentation on the TailwindCSS site https://tailwindcss.com/docs/guides/vue-3-vite and I think I'm missing some manipulations to do

So I did "npx tailwindcss init -p" to create the tailwind.config.js and postcss.config.js files, but after this manipulation, the npm run serve gave me the same error as before.

I really don't understand ... It tells me to need PostCSS8 even though I have version8.3.11

I did some tests, I tried to create the tailwind.config.js and postcss.config.js files myself, no problem with tailwind.config.js, but from the moment I create the postcss.config.js file and start npm run serve the error message comes back.

I wonder if we can do a VueJS project with Tailwind without Vite now...

Thank you for your help ! :)