would like to know this too.
If you have the same question as the original poster, it's not a matter of the Browser Source going fullscreen automatically, but the YouTube video at the given url. If you want to experiment with a Browser Source and a url with (almost) fullscreen video, take a look at
Y.CO (no endorsement in any way
loll).
A quick Google search provided several pages claiming to have YouTube url syntax for full screen... that did not seem to work.
As a workaround you might want to experiment with a local file.
call-it-anything.html
<html>
<body>
<iframe width="100%" height="100%" src="https://www.youtube.com/embed/qmge3G5VK6U" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen>
</iframe>
</body>
</html>
The iframe part comes straight from YouTube: below the video click
Share,
Embed. Only adapt width and height to 100%.
You'd still need to
Interact with the Browser Source to start the video though.