There is no 'proper' way to do it on Android, hence no API support yet.
The workaround we used in my company -
On first login, store screenheight in localstorage.
By screenHeight i mean document.documentElement.clientHeight before page loads, since then doc grows and its not accurate measure for real available screen height.
Whenever user logs in next time - check current screenheight vs stored - if it becomes bigger, the user has gone fullscreen.
There is no scenario upon which it can become smaller, IF YOU DO store FIRST TIME value for screen height.
Caveat - user that will clean cash.
We chose to ignore that, since most users don't do it or do it relatively rarely, and it will suffice(in our opinion) for some time until there will be API fix for this( hopefully there will be :) )
Option b - check available screenheight vs device screen height, the matchup for a few test devices & browser modes showed some pattern( available height < 70 in webapp) - i strongly believe a wider comparison can get values that will suffice for 90% of devices in 90% cases.
All of this is a workaround, of course, i m not pretending its a solid stable way to get to desired functionality - but for us it worked, so i hope this helps somebody else who fought this bug(cant call missing such crucial api feature other way). Good luck :)