The real issue people should be discussing is Apple not supporting PWAs, or in fact, any browser engine other than Safari on iPhones. It's the real blocker to wider adoption of PWAs (and many other features!)
Until that happens, whether Firefox desktop / other platforms support this specific behaviour (Single-Site Browser) is a bit moot as it's an edge case compared to 50% of mobile users.
You can have fullscreen apps that run offline, launched from the home screen.
However, you can not trigger an installation prompt like on Android.
You can't trigger a native prompt automatically, but you can detect if your web app is installed as a PWA. With that information you can show instructions.
This is not true, it's a misconception about how the seven-day-counter works when the app is installed on the home screen.
Nevertheless, persistent data is a concern, because the standards do not specify how long data must be kept, so it could get wiped at some point, for example when the device is low on disk storage.
Why anyone considers iOS any more than a terrible joke is beyond me.