Vite build for a custom React library: module [...] was resolved to [...] but --jsx is not set

I'm working on a monorepo and I'm trying to create a package that would be a React ui-kit library. For now, I've been trying to export a custom button component and building the ESM et CJS modules with Vite.

However when I'm building it with Vite, I get this error :

Module './components/button.js' was resolved to '[...]/libs/ui/src/components/button.tsx', but '--jsx' is not set.

Here is the component

// src/components/button.tsx
import React, { ComponentProps } from 'react'
import "../index.css";
 
export function Button(props: Omit<ComponentProps<'button'>, 'className'>) {
  return <button className="bg-blue-500 text-white px-4 py-2 rounded" {...props} />;
}

// src/main.ts
export { Button } from './components/button.js';

And here is the Vite config as well as the tsconfig:

// vite.config.ts
import { defineConfig } from 'vite'
import react from '@vitejs/plugin-react'
// export type definition files
import dts from 'vite-plugin-dts'

import path from 'path'

import packageJson from './package.json'

export default defineConfig({
  root: '/',
  plugins: [react(), dts({ include: 'src' })],
  build: {
    // build package as a library
    lib: {
      entry: path.resolve(__dirname, 'src/index.ts'),
      // es = ES module
      formats: ['es', 'cjs']
    },
    rollupOptions: {
      // avoid bundling react and react-dom
      // as they will be already required and bundled by the user app
      // using this application
      external: ['react', 'react-dom', 'react/jsx-runtime', 'tailwindcss']
    },
    sourcemap: true
  }
})

// tsconfig.json
{
  "extends": "../../tsconfig.json",
  "include": ["src/**/*.ts", "src/**/*.tsx"],
  "compilerOptions": {
    "module": "NodeNext",
    "moduleResolution": "NodeNext",
    "jsx": "react-jsx",
    "resolveJsonModule": true
  },
  "exclude": ["node_modules/"]
}

If I do not set react/jsx-runtime as external dependency, I get another error:

error during build:
[vite]: Rollup failed to resolve import "react/jsx-runtime" from "[...]/libs/ui/src/components/button.tsx".

I do not know what's wrong in my config ?