Define perfectly.
If put on full screen there is a non-obvious way to go back in browser history. @pmusaraj created a navigation footer to work around it.
Every time you switch back to the PWA it does a full load with a blank screen flash.
There is no offline browsing because Same site cookies in Safari have a long standing bug 200345 – SameSite cookies missing after Safari Tab recovery
If you want full screen pwa on your site for iOS you can enable it using Back button in iOS PWA - #92 by Falco. Please update us about the experience.