I did some quick testing with this and it seems like there’s not a quick solution.
From my testing, iOS 15 seemed a bit finicky – Apple has a custom property for setting the status bar color, but iOS 15 doesn’t respect the values that are officially published by Apple (though it does work with some undocumented values). And unfortunately, iOS 15 only respects those values if we don’t set the standard ‘theme’ color which is a broader industry standard respected by a much wider set of browsers… which means trying to get a black status bar with just iOS 15 seems to impact pretty much every other browser in a negative way.
I’ve converted this topic into a feature request so other people can vote to express interest.
Edit: Not sure if you’ve tried one of the apps like Kiosker, Kiosk Pro, or tKiosk but I would be curious what the status bar looks like on those with iOS 15: How to switch from Android/Fire to Apple / iOS / iPad Pro? - #2 by josh