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. Please update us about the experience.