Sorry, I wasn’t replying to you. Your post reminded me that it hadn’t been mentioned here before, and so I announced it explicitly for people who didn’t know.
I don’t think CSS or JS can do it, since the status bar is outside the app. If the developers add full screen mode to tablets, I expect it would hide the status bar as it does on phones. For now, the feature request Hide/show top bar(s) when keyboard appears/disappears stands for adding full screen mode to tablets, but it might be worth making a separate request. That thread includes workarounds that hide the top bars on tablets, but not the OS status bar.