Use Streaming Online Video/Live As Source In OBS Studio
This would be possible using OBS's BrowserSource.

First, find the embed code for the stream (in YouTube you can click "Share" and then "Embed"). Find the src="" and copy the URL that's inside the quotes. In OBS, create a new Browser. Paste the previously copied URL into the URL field, and set the Width and Height to your canvas size (or your preferred size).

If you need to press a play button, you can right-click the Browser and click Interact.

I hope this helps!