This would be good if we can provide specific URL patterns that would do this automatically.

However for now you can hack it with Grease Monkey

// ==UserScript==
// @name Redirect and Close Tab
// @namespace http://your.namespace.here
// @version 1.0
// @description Change the URL of the current page and close the tab
// add your stuff
// @match https://dev.azure.com/*
// @grant none
// ==/UserScript==

(function() {
'use strict';

var currentURL = window.location.href;
var newURL = "microsoft-edge:" + currentURL;
window.location.href = newURL;
window.close();
})();