Node.js spawn child process stderr not working

I am trying to write a simple node program that spawns a child process in a separate window (that can be viewed) and then, on program completion, prints the stderr messages. Currently testing on Windows.

I made a parent.js file:

const { spawnSync } = require('child_process')

const child = spawnSync('node child.js', [], { shell: true, detached: true })
console.log(child)

I am using both 'shell' and 'detached' parameters because it was the only way I could find to open and view a new terminal window.

Then, in child.js:

let count = 0
setInterval(() => {
    console.log('test', count)
    count++
    if (count == 4) {
        process.stderr.write('an error occurred!')
        process.exit(1)
    }
}, 1000)

Which is a very simple test program that after 4 seconds writes to stderr and then exits with an error code.

After running, however, I receive this output:

{
  status: 1,
  signal: null,
  output: [ null, <Buffer >, <Buffer > ],
  pid: 3500,
  stdout: <Buffer >,
  stderr: <Buffer >
}

So, while the error code registered correctly, stderr is an empty buffer. What am I doing wrong? What else could I do to achieve what I'm looking for? (run a node child process in a separate window and get errors from parent).

Any help is really appreciated. Thank you!