It’s only compatible with Google Chrome, Microsoft Edge and other Chromium-based browsers afaik.
I assume its not possible, otherwise anyone would have done that already. From what I read through online research, it looks like Xbox Cloud is using an API for Cloud streaming by Google. And only Chromium based browser have this implemented and Firefox does not support it. If this is correct, then there is nothing you can do about it. People try to make Xbox Cloud work with Firefox for a long time now, without success.
Not this streaming is not just showing video files like YouTube. Game streaming involves gamepad (or other input) in realtime to coordinate with the server. Therefore the browser has to support these functionalities.
Not to my knowledge but there are dedicated wrapper projects if you’d rather not use a full chromium based browser
