How to add web app icon png to root document folder? To specify an icon for the entire website (every page on the website),
  place an icon file in PNG format in the root document folder called
  apple-touch-icon.png


Exactly how do I do this in Drupal 8?  

Yes, my site adds lots of different touch icons to the html.html.twig template in an assortment of different sizes for Android, Apple, and MS Tiles but all this does not have precisely the effect I want for my web app. For further info see Apple docs here.
place an icon file in PNG format in the root document folder called apple-touch-icon.png


Literally that - put a file called apple-touch-icon.png in your web root. Drupal doesn't affect static files, it won't interfere.