Salesforce OAuth 2.0 implementation CRA

Question

I am attempting to grab the authorization code appended to the redirect uri using the OAuth2.0 Web Server Flow for Web App Integration seen here: https://help.salesforce.com/s/articleView?id=sf.remoteaccess_oauth_web_server_flow.htm&type=5

When a user hits a button, I am opening a child window where the user authorizes via OAuth and is then redirected to the callback uri upon successful verification, etc. Is there a way to access the url of the child window and grab the authorization code as well as close the child window upon successful verification. My code is as follows:

const Dashboard = () => {
  const openWindow = () => {
    const newWindow = window.open(
      `${salesforceAppUrl}/services/oauth2/authorize?&response_type=code&client_id=${clientId}&redirect_uri=https://login.salesforce.com/services/oauth2/success`,
      '',
      'width=850,toolbar=1,resizable=1,scrollbars=yes,height=700,top=100,left=100'
    )
    console.log(newWindow)
  }

  return <button onClick={openWindow}>test</button>
}

export default Dashboard

I am wondering if I am going about this correct way/looking for guidance on the proper way to go about grabbing the authorization code from the redirect uri when a successfully auths. Any and all suggestions would be greatly appreciated.