favicon.ico is largely deprecated but is still supported
Browsers will actively use <link rel="icon"> if found, superceding favicon.ico, this is why the wrong favicon is seen in browser
There is no way to specifically serve one icon for the browser and one icon for mobile devices, at least on Android.
There is the apple-touch-icon, but in NodeBB, we just lump it along with the "home screen icon" setting.
So I think you're going to want to just upload the same image to both fields