I've enabled full screen mode on itch.io. (Itch.io's full screen, not Unity's).
Does not work. The "fullscreen" is not fullscreen. Oh, the browser goes fullscreen and it is different than regular fullscreen with F11.
But try pressing ctrl + and - . The browser zoom setting still get's applied. Anyone not browsing with 100% zoom will not see the game in fullscreen.
I randomly tried a few other games that are Unity and web. Some work, some do not even have a fullscreen button. There even seems to be an issue with staying "fullscreen", but rendering the game to a lower resolution. The Unity fullscreen button seemed to be the most reliable.
It is a shame that developers have to do this manually and is not handled in a plug&play fashion easy to implement. And a shame it is, because resizing screen resolution is old, not new. With crt displays this was common. The whole display would be analogous set to a new hardware resolution. You could never be sure what the pixel resolution would be. One would excpect time tested solutions to this kind of problems.