Newest game streaming app update has made console streaming almost unplayable

That is because when you stream something that you are playing online it kills your internet connection. I tried to stream once and it made the game I was playing virtually unplayable. Have not done it since.

We can't know what the upcoming Xbox Series X features for streaming are just now.

Microsoft had their own streaming service called "Mixer", that they shut down just yesterday on July 22nd. And for that service, they had streaming built right into the Xbox One console. You'd just set up your stream from the console guide, and could stream
to Mixer.

Twitch has made a separate app that you could install on your Xbox One, and set up streaming to Twitch from the console.

Unfortunately for YouTube, there was no app or built in support, as YouTube/Google hasn't provided such an app on Xbox.

If you really want/have to stream your Xbox gameplay to YouTube, the currently only known way is to have a PC with HDMI capturing hardware and a streaming software like OBS or XSplit to stream that video capture from the PC to YouTube.

You can't connect the Xbox 360 to the Xbox App. Only the Xbox One can stream to the Xbox App.

Long explanation:

The Xbox One has specifically resources reserved to record or stream the console's video output, so you can stream to Beam or Twitch, or record your Gameplay.

The Xbox 360 does not have these resources. And since compressing and streaming video requires a lot of CPU power, and the Xbox 360 is uses nearly 98% CPU resources for rendering games (the rest is used for Guide, Parties and background music), the Xbox
360 also can't get an update to allow game streaming.

In short: It's not possible to connect the Xbox App to the 360.

In what way do you mean?

Watch a stream while playing a game or stream the PC game you are playing?

If it's stream the game you are playing, no it's not possible. You can only use the Twitch app on the Xbox to stream Xbox console games.

To watch a stream on the console, it's easy, just launch the app, then log in, and find a stream you want to watch, then start a game on your PC.

You need to stream your console to your laptop (Has to have Windows 10) with The Xbox Console Companion app. Start the Xbox One, then start the Console companion app, then select the connect icon on the left side of the app, and your console should show,
just select it, and select stream, that will then stream your console to your laptop.