A possible solution would be to use postcss-url:

import postcssurl from 'postcss-url';

postcss({
 ..., // postcss options
 plugins: [
   postcssurl({
     url: 'inline',
   }),
 ],
}),

I am not not sure if it is possible with rollup-plugin-postcss, Try using “image-to-base64” npm it’s very simple, Download command :

npm i -S image-to-base64

Example :

const imageToBase64 = require('image-to-base64');
//or
//import imageToBase64 from 'image-to-base64/browser';

imageToBase64("path/to/file.jpg") // Path to the image
    .then(
        (response) => {
            console.log(response); // "cGF0aC90by9maWxlLmpwZw=="
        }
    )
    .catch(
        (error) => {
            console.log(error); // Logs an error if there was one
        }
    )

There is more examples here

https://www.npmjs.com/package/image-to-base64

If you need more help you can reply to this comment.

You can use postcss-inline-base64

Here is a working example based on this rollup starter:

import resolve from '@rollup/plugin-node-resolve';
import commonjs from '@rollup/plugin-commonjs';
import { terser } from 'rollup-plugin-terser';
import path from 'path'

import postcss from 'rollup-plugin-postcss'
import base64Inliner from 'postcss-inline-base64'


// `npm run build` -> `production` is true
// `npm run dev` -> `production` is false
const production = !process.env.ROLLUP_WATCH;
const __dirname = path.resolve();
const baseDir = path.join(__dirname, 'public')


export default {
    input: 'src/main.js',
    output: {
        file: 'public/bundle.js',
        format: 'iife', // immediately-invoked function expression — suitable for <script> tags
        sourcemap: true
    },
    plugins: [
        postcss({
            extensions: ['.css'],
            extract: path.resolve('public/styles.css'),
            plugins: [base64Inliner({ baseDir })]
        }),
        ...
    ]
};

I then created a css file in the src folder:

body {
    background: url('b64---./images/test.png---');
}

In index.js:

import "./styles.css";

In index.html

....
<title>rollup-starter-app</title>
<link href="styles.css" rel="stylesheet" />
....

I was able to get: