Hmm. Thinking this through further, there are actually pretty deep issues with putting fullscreen mode under scripted control. In the native version, it's simple. Web browsers, however, can only request a change in fullscreen mode in direct response to user input events. I can probably slip in a keyboard shortcut for web-decker, but that doesn't help users on phones, and to make matters worse iPhones explicitly do not support the browser APIs necessary to enter fullscreen at all.
Viewing post in Web-decker fullscreen with protected decks
Similar, but even more rigid; on the JS side, the change must happen directly in the call chain from a user-initiated event handler, like a mouse-click or a keypress, but Lil scripts run asynchronously in the background and do not inherently have the necessary connection to input events, even if they usually are user-initiated in some way.
It's a bit inelegant, but the best compromise I can come up with is to require the user to confirm via a modal when they wish to enter fullscreen mode in web-decker, much like the confirmation modal when you want to "read[]" a file from a script. Exiting fullscreen mode doesn't come with as many strings attached.

This is available to play right right now: https://beyondloom.com/decker/tour.html
For convenience, a paste-able usage example:
%%WGT0[{"name":"button2","type":"button","size":[112,30],"pos":[25,41],"script":"on click do\n me.text:if sys.fullscreen\n sys.fullscreen:0\n \"Enter Fullscreen\"\n else\n sys.fullscreen:1\n \"Exit Fullscreen\"\n end\nend","text":"Enter Fullscreen"}]
As previously noted, this is all at best a vague suggestion to web browsers, so it's possible that on some devices it simply won't do anything.