Out of curiosity. Is there any way to stream directly to a website without using a 3rd party program
of course... though, it depends on what you mean
The "Yes" answer applies to sending straight from a camera to a streaming site (ie RTMP straight from camera). in essence, the streaming software is running on the camera
If you are asking about sending from your computer - no, not really. What that would require is a native Operating System capability to send a video output in a streaming protocol. And Operating System vendors know better than to waste their time doing such a thing. It woudl be truly silly on their part to even attempt such a thing. There are lots of driver options (3rd party) to enable such, including both major video card makers.
Now, if you want sophisticated, powerful compositing (bring together of multiple pieces in exactly the way you want them), then OBS or similar is required