First note that this only applies when you choose "Add to Home Screen" from Mobile Safari's sharing panel and open the page as an app.
The cover notches setting is at odds with the status bar setting when using an iPhone with notches. If you choose cover notches, then the web page will be placed up to the edge of the screen (on models with notches), and no status bar is shown. If you do not have cover notches, then you'll be able to see the result of that setting.
Yup, either way you will still see the status bar items, even if cover notches prevents there from being a status bar....