In window B you set a cookie and in window A you create a setTimeout function that every "x" milliseconds check if there are any new cookie.

Look at this: Javascript communication between browser tabs/windows

input.keydown(function(event){
    if (event.keyCode === 9) {
        event.preventDefault();
    }
})

On keyup is too late, you need to call the event on keydown. That worked for me.

You can add an event listener to the document like so.

document.addEventListener('keyup', function(event) {
  if (event.keyCode == 9) {
     whenEmpty();
  }
});

This will listen for any keyup (keyboard button released) events, and then in the if check what the keycode of the pressed button was. 9 is the keycode for Tab. If you want to pass the field to the function, you could also add the event listener to the input itself. Then access it with event.target

I got this one working with the beforeunload method

Went some like this:

useEffect(() => {
  window.addEventListener("beforeunload", () => {
    if (chatToEmailServer.chatToServer.length > 0) {
      emailChatHistory();
      setFirstMsg(true);
    }
  });
}, [chatToEmailServer.chatToServer, firstMsg]);

^^^ This is working, but it gives me warning on the code for dependencies.

Trying to fix the dependencies error is something in the backburner because include the emailChatHistory() in the dependencies, then I have to dig all through de code and fix communication with the API and a few other things.... basically it opens another chain of errors that I couldn't figured out.... so, until it breaks, or when I got time, I might change the code later.

If I get you correctly, you want to know when a tab/window is effectively closed. Well, AFAIK the only way in JavaScript to detect that is to use either onunload or onbeforeunload events.

Unfortunately (or fortunately?), those events are also fired when you leave a site over a link or your browsers back button. So this is the best answer I can give, I don't think you can natively detect a pure close in JavaScript. Correct me if I'm wrong here.