HTML5 Full Screen Extension
About
As you probably know, window_set_fullscreen() does not work on HTML5. So after searching online, I basically copy/pasted a small Javascript code for a GMS1 extension found in this forum post (full credit to the original author), in order to create a button that is added on top of the game canvas (I chose the bottom right corner but you can change that on the provided script), that lets you toggle full screen on or off. Check out the demo "game" above.
By the way, the itch.io option to include a fullscreen button makes the browser full screen but does not actually scale the canvas.
I also added a small utility function, to check whether the game is in full screen that works cross-platform, including HTML5.
I included a button sprite, but obviously you can change that to whatever you want.
Disclaimer
Tested on GameMaker 2022.8+ (uses a call_later call) on current versions of Opera GX, Chrome and Edge. Firefox does not seem to work as expected. Provided as is - expect little to no support, hopefully you won't need it :)
I also included the demo GameMaker project if you want/need, on a separate file.