As you have discovered, browser compatibility is a big drawback. After all, this is something very new.
However, since you’re working in JavaScript, you have far more options available to you than if you were just using CSS.
For example:
if( window.innerHeight == screen.height) {
// browser is fullscreen
}
You can also check for some slightly more loose comparisons:
if( (screen.availHeight || screen.height-30) <= window.innerHeight) {
// browser is almost certainly fullscreen
}