Workaround for banking authentication redirect to prevent session loss / need for session restorage

Question

My question is kind of a follow-up to this somewhat old post, which is why I though of asking here, instead of just asking via comment there.

My question is straightforward: I have an online platform with very tight session restrictions (samesite, httponly, short lifetimes, etc.), and while a user is logged into the platform, they may execute payments. These payments may redirect them to an intermediary foreign domain and then back to mine for authentication. Without a workaround (that I've coded and it works) for the session restorage, the session gets lost and the process breaks.

Even though I have a working workaround; I wondered if it is not possible to open the redirect page in a new tab via js (because the redirect has to work in js at the current stage anyway), confirm the payment, then, when the payment gets confirmed, close the banking tab and do the according refreshes on the platform tab. Is this possible via js ? The problem I see with the linked solution is:

btn.onclick = () => {
  const win = window.open(
      'http://www.stackoverflow.com',
      'Secure Payment');
  const timer = setInterval(() => {
    if (win.closed) {
      clearInterval(timer);
      alert('"Secure Payment" window closed!');
    }
  }, 500);
}

How can I know when the client finished the authentication in the other tab, + prevent the redirect that will automatically triggered in that case, to the redirect target post-authentication that you normally provide when requesting the payment? Is there a way to track all of this in js? Because I don't see any...?